{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T13:31:48Z","timestamp":1780579908187,"version":"3.54.1"},"reference-count":55,"publisher":"American Mathematical Society (AMS)","issue":"307","license":[{"start":{"date-parts":[[2017,12,21]],"date-time":"2017-12-21T00:00:00Z","timestamp":1513814400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-CE40-0005"],"award-info":[{"award-number":["ANR-15-CE40-0005"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady nonlinear Leray\u2013Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case. The convergence analysis is carried out using a compactness technique. Extending this technique to HHO methods has prompted us to develop a set of discrete functional analysis tools whose interest goes beyond the specific problem and method addressed in this work: (direct and) reverse Lebesgue and Sobolev embeddings for local polynomial spaces,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript p\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^{p}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -stability and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper W Superscript s comma p\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>W<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>s<\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">W^{s,p}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -approximation properties for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^{2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -projectors on such spaces, and Sobolev embeddings for hybrid polynomial spaces. Numerical tests are presented to validate the theoretical results for the original method and variants thereof.\n                  <\/p>","DOI":"10.1090\/mcom\/3180","type":"journal-article","created":{"date-parts":[[2016,5,26]],"date-time":"2016-05-26T08:34:49Z","timestamp":1464251689000},"page":"2159-2191","source":"Crossref","is-referenced-by-count":87,"title":["A Hybrid High-Order method for Leray\u2013Lions elliptic equations on general meshes"],"prefix":"10.1090","volume":"86","author":[{"given":"Daniele","family":"Di Pietro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Droniou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2016,12,21]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1051\/m2an:2004045","article-title":"Finite volume schemes for the \ud835\udc5d-Laplacian on Cartesian meshes","volume":"38","author":"Andreianov, Boris","year":"2004","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/s00211-005-0591-8","article-title":"Besov regularity and new error estimates for finite volume approximations of the \ud835\udc5d-Laplacian","volume":"100","author":"Andreianov, Boris","year":"2005","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1093\/imanum\/dri047","article-title":"On the finite-volume approximation of regular solutions of the \ud835\udc5d-Laplacian","volume":"26","author":"Andreianov, Boris","year":"2006","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/num.20170","article-title":"Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes","volume":"23","author":"Andreianov, Boris","year":"2007","journal-title":"Numer. Methods Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0749-159X","issn-type":"print"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10092-014-0107-y","article-title":"Mimetic finite difference approximation of quasilinear elliptic problems","volume":"52","author":"Antonietti, Paola F.","year":"2015","journal-title":"Calcolo","ISSN":"https:\/\/id.crossref.org\/issn\/0008-0624","issn-type":"print"},{"issue":"3","key":"6","doi-asserted-by":"publisher","first-page":"A1417--A1439","DOI":"10.1137\/120877246","article-title":"\u210e\ud835\udc5d-version composite discontinuous Galerkin methods for elliptic problems on complicated domains","volume":"35","author":"Antonietti, Paola F.","year":"2013","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"6","key":"7","doi-asserted-by":"publisher","first-page":"3505","DOI":"10.1137\/120888223","article-title":"Multiscale hybrid-mixed method","volume":"51","author":"Araya, Rodolfo","year":"2013","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1137\/0719052","article-title":"An interior penalty finite element method with discontinuous elements","volume":"19","author":"Arnold, Douglas N.","year":"1982","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s00211-013-0562-4","article-title":"On the \ud835\udc3b\u00b9-stability of the \ud835\udc3f\u2082-projection onto finite element spaces","volume":"126","author":"Bank, Randolph E.","year":"2014","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"10","isbn-type":"print","first-page":"1","article-title":"Finite element approximation of degenerate quasilinear elliptic and parabolic problems","author":"Barrett, J. W.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/058222568X"},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.jcp.2011.08.018","article-title":"On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations","volume":"231","author":"Bassi, F.","year":"2012","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1142\/S0218202512500492","article-title":"Basic principles of virtual element methods","volume":"23","author":"Beir\u00e3o da Veiga, L.","year":"2013","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1137\/120874746","article-title":"Virtual elements for linear elasticity problems","volume":"51","author":"Beir\u00e3o da Veiga, L.","year":"2013","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"14","doi-asserted-by":"crossref","unstructured":"H. Blatter, Velocity and stress fields in grounded glacier: a simple algorithm for including deviator stress gradients, J. Glaciol. 41 (1995), 333\u2013344.","DOI":"10.3189\/S002214300001621X"},{"issue":"11","key":"15","first-page":"1159","article-title":"Unicit\u00e9 de la solution de certaines \u00e9quations elliptiques non lin\u00e9aires","volume":"315","author":"Boccardo, Lucio","year":"1992","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"issue":"237","key":"16","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1090\/S0025-5718-01-01314-X","article-title":"On the stability of the \ud835\udc3f\u00b2 projection in \ud835\udc3b\u00b9(\u03a9)","volume":"71","author":"Bramble, James H.","year":"2002","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"17","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1137\/S0036142902401311","article-title":"Poincar\u00e9-Friedrichs inequalities for piecewise \ud835\udc3b\u00b9 functions","volume":"41","author":"Brenner, Susanne C.","year":"2003","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"18","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387759333","edition":"3"},{"issue":"4","key":"19","doi-asserted-by":"publisher","first-page":"1227","DOI":"10.1051\/m2an\/2013138","article-title":"Basic principles of mixed virtual element methods","volume":"48","author":"Brezzi, F.","year":"2014","journal-title":"ESAIM Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/2822-7840","issn-type":"print"},{"issue":"10","key":"20","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1142\/S0218202505000832","article-title":"A family of mimetic finite difference methods on polygonal and polyhedral meshes","volume":"15","author":"Brezzi, Franco","year":"2005","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"4","key":"21","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1093\/imanum\/drn038","article-title":"Compact embeddings of broken Sobolev spaces and applications","volume":"29","author":"Buffa, Annalisa","year":"2009","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"issue":"17-18","key":"22","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1016\/j.crma.2008.07.005","article-title":"Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian","volume":"346","author":"Burman, Erik","year":"2008","journal-title":"C. R. Math. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/1631-073X","issn-type":"print"},{"issue":"237","key":"23","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1090\/S0025-5718-01-01316-3","article-title":"Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thom\u00e9e criterion for \ud835\udc3b\u00b9-stability of the \ud835\udc3f\u00b2-projection onto finite element spaces","volume":"71","author":"Carstensen, Carsten","year":"2002","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"8","key":"24","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.crma.2007.02.007","article-title":"Uniqueness results for pseudomonotone problems with \ud835\udc5d>2","volume":"344","author":"Casado-D\u00edaz, Juan","year":"2007","journal-title":"C. R. Math. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/1631-073X","issn-type":"print"},{"issue":"5","key":"25","doi-asserted-by":"publisher","first-page":"1676","DOI":"10.1137\/S0036142900371003","article-title":"An a priori error analysis of the local discontinuous Galerkin method for elliptic problems","volume":"38","author":"Castillo, Paul","year":"2000","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"3","key":"26","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1051\/m2an\/2015051","article-title":"Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods","volume":"50","author":"Cockburn, Bernardo","year":"2016","journal-title":"ESAIM Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/2822-7840","issn-type":"print"},{"issue":"2","key":"27","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","article-title":"Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems","volume":"47","author":"Cockburn, Bernardo","year":"2009","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"178","key":"28","doi-asserted-by":"publisher","first-page":"521","DOI":"10.2307\/2007825","article-title":"The stability in \ud835\udc3f_{\ud835\udc5d} and \ud835\udc4a\u00b9_{\ud835\udc5d} of the \ud835\udc3f\u2082-projection onto finite element function spaces","volume":"48","author":"Crouzeix, M.","year":"1987","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"29","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00547-7","volume-title":"Nonlinear functional analysis","author":"Deimling, Klaus","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/3540139281"},{"issue":"5","key":"30","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1137\/140993971","article-title":"A discontinuous-skeletal method for advection-diffusion-reaction on general meshes","volume":"53","author":"Di Pietro, Daniele A.","year":"2015","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"271","key":"31","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1090\/S0025-5718-10-02333-1","article-title":"Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations","volume":"79","author":"Di Pietro, Daniele A.","year":"2010","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"32","doi-asserted-by":"crossref","unstructured":"D. A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, Math\u00e9matiques & Applications, vol. 69, Springer-Verlag, Berlin, 2012.","DOI":"10.1007\/978-3-642-22980-0"},{"issue":"4","key":"33","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1515\/cmam-2014-0018","article-title":"An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators","volume":"14","author":"Di Pietro, Daniele A.","year":"2014","journal-title":"Comput. Methods Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1609-4840","issn-type":"print"},{"issue":"291","key":"34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0025-5718-2014-02861-5","article-title":"An extension of the Crouzeix-Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow","volume":"84","author":"Di Pietro, Daniele A.","year":"2015","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"35","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1137\/S0036141091217731","article-title":"On a nonlinear parabolic problem arising in some models related to turbulent flows","volume":"25","author":"Diaz, Jesus Ildefonso","year":"1994","journal-title":"SIAM J. Math. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1410","issn-type":"print"},{"issue":"6","key":"36","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1051\/m2an:2007001","article-title":"Finite volume schemes for fully non-linear elliptic equations in divergence form","volume":"40","author":"Droniou, J\u00e9r\u00f4me","year":"2006","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"1","key":"37","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s00211-006-0034-1","article-title":"A mixed finite volume scheme for anisotropic diffusion problems on any grid","volume":"105","author":"Droniou, J\u00e9r\u00f4me","year":"2006","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"38","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1002\/num.20333","article-title":"Study of the mixed finite volume method for Stokes and Navier-Stokes equations","volume":"25","author":"Droniou, J\u00e9r\u00f4me","year":"2009","journal-title":"Numer. Methods Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0749-159X","issn-type":"print"},{"key":"39","unstructured":"J. Droniou, R. Eymard, T. Gallou\u00ebt, C. Guichard, and R. Herbin, The gradient discretisation method: a framework for the discretisation and numerical analysis of linear and nonlinear elliptic and parabolic problems, preprint, https:\/\/hal.archives-ouvertes.fr\/hal-01382358, 2016."},{"issue":"2","key":"40","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1142\/S0218202510004222","article-title":"A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods","volume":"20","author":"Droniou, J\u00e9r\u00f4me","year":"2010","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"13","key":"41","doi-asserted-by":"publisher","first-page":"2395","DOI":"10.1142\/S0218202513500358","article-title":"Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations","volume":"23","author":"Droniou, Jerome","year":"2013","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"150","key":"42","doi-asserted-by":"publisher","first-page":"441","DOI":"10.2307\/2006095","article-title":"Polynomial approximation of functions in Sobolev spaces","volume":"34","author":"Dupont, Todd","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"43","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1093\/imanum\/drn084","article-title":"Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces","volume":"30","author":"Eymard, R.","year":"2010","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"issue":"249","key":"44","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1090\/S0025-5718-04-01652-7","article-title":"A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems","volume":"74","author":"Girault, Vivette","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"45","series-title":"Springer Series in Computational Physics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12613-4","volume-title":"Numerical methods for nonlinear variational problems","author":"Glowinski, Roland","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0387124349"},{"issue":"1","key":"46","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1051\/m2an:2003012","article-title":"Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology","volume":"37","author":"Glowinski, Roland","year":"2003","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"key":"47","isbn-type":"print","first-page":"659","article-title":"Benchmark on discretization schemes for anisotropic diffusion problems on general grids","author":"Herbin, Rapha\u00e8le","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9781848210356"},{"issue":"1","key":"48","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1137\/S0036142996297199","article-title":"A nonconforming finite element method for the stationary Navier-Stokes equations","volume":"35","author":"Karakashian, Ohannes A.","year":"1998","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"49","unstructured":"A. Lasis and E. S\u00fcli, Poincar\u00e9-type inequalities for broken Sobolev spaces, Technical Report 03\/10, Oxford University Computing Laboratory, Oxford, England, 2003."},{"key":"50","doi-asserted-by":"crossref","first-page":"97","DOI":"10.24033\/bsmf.1617","article-title":"Quelques r\u00e9sulatats de Vi\u0161ik sur les probl\u00e8mes elliptiques nonlin\u00e9aires par les m\u00e9thodes de Minty-Browder","volume":"93","author":"Leray, Jean","year":"1965","journal-title":"Bull. Soc. Math. France","ISSN":"https:\/\/id.crossref.org\/issn\/0037-9484","issn-type":"print"},{"key":"51","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1016\/j.jcp.2014.04.021","article-title":"A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation","volume":"272","author":"Lipnikov, K.","year":"2014","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"2","key":"52","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/PL00005470","article-title":"Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of \ud835\udc5d-Laplacian","volume":"89","author":"Liu, Wenbin","year":"2001","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"53","doi-asserted-by":"publisher","first-page":"1038","DOI":"10.1073\/pnas.50.6.1038","article-title":"on a \u201cmonotonicity\u201d method for the solution of non-linear equations in Banach spaces","volume":"50","author":"Minty, George J.","year":"1963","journal-title":"Proc. Nat. Acad. Sci. U.S.A.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-8424","issn-type":"print"},{"key":"54","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.cam.2012.10.003","article-title":"A weak Galerkin finite element method for second-order elliptic problems","volume":"241","author":"Wang, Junping","year":"2013","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"289","key":"55","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.1090\/S0025-5718-2014-02852-4","article-title":"A weak Galerkin mixed finite element method for second order elliptic problems","volume":"83","author":"Wang, Junping","year":"2014","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2017-86-307\/S0025-5718-2016-03180-4\/mcom3180_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/www.ams.org\/mcom\/2017-86-307\/S0025-5718-2016-03180-4\/S0025-5718-2016-03180-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2017-86-307\/S0025-5718-2016-03180-4\/S0025-5718-2016-03180-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:18:05Z","timestamp":1776799085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2017-86-307\/S0025-5718-2016-03180-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,21]]},"references-count":55,"journal-issue":{"issue":"307","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["S0025-5718-2016-03180-4"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3180","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2016,12,21]]}}}