{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:10:33Z","timestamp":1776838233655,"version":"3.51.2"},"reference-count":55,"publisher":"American Mathematical Society (AMS)","issue":"349","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101115663"],"award-info":[{"award-number":["101115663"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC Synergy grant NEMESIS ("],"award-info":[{"award-number":["ERC Synergy grant NEMESIS ("]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101115663"],"award-info":[{"award-number":["101115663"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC Synergy grant NEMESIS ("],"award-info":[{"award-number":["ERC Synergy grant NEMESIS ("]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We present a complete numerical analysis for a general discretization of a coupled flow\u2013mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix\u2013fracture interfaces, as well as nonlinear poromechanical coupling. Fractures are described as planar surfaces, yielding the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. The model accounts for discontinuous fluid pressures at matrix\u2013fracture interfaces in order to cover a wide range of normal fracture conductivities.<\/p>\n                  <p>\n                    The numerical analysis is carried out in the Gradient Discretization framework (see J. Droniou, R. Eymard, T. Gallou\u00ebt, C. Guichard, and R. Herbin [\n                    <italic>The gradient discretisation method<\/italic>\n                    , Springer, Cham, 2018]), encompassing a large family of conforming and nonconforming discretizations. The convergence result also yields, as a by-product, the existence of a weak solution to the continuous model. A numerical experiment in 2D is presented to support the obtained result, employing a Hybrid Finite Volume scheme for the flow and second-order finite elements (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper P 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {P}_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) for the mechanical displacement coupled with face-wise constant (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper P 0\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb P_0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions.\n                  <\/p>","DOI":"10.1090\/mcom\/3949","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T11:52:46Z","timestamp":1709812366000},"page":"2103-2134","source":"Crossref","is-referenced-by-count":1,"title":["Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix\u2013fracture interfaces"],"prefix":"10.1090","volume":"93","author":[{"given":"Francesco","family":"Bonaldi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00e9r\u00f4me","family":"Droniou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roland","family":"Masson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"J. 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Geomath.","ISSN":"https:\/\/id.crossref.org\/issn\/1869-2672","issn-type":"print"},{"key":"3","doi-asserted-by":"publisher","first-page":"Paper No. 110452, 27","DOI":"10.1016\/j.jcp.2021.110452","article-title":"A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion","volume":"441","author":"Aghili, Joubine","year":"2021","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"4","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.matcom.2016.10.005","article-title":"A reduced fracture model for two-phase flow with different rock types","volume":"137","author":"Ahmed, Elyes","year":"2017","journal-title":"Math. Comput. 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