{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:50:55Z","timestamp":1759837855560,"version":"3.40.3"},"publisher-location":"Cham","reference-count":36,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030504359"},{"type":"electronic","value":"9783030504366"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-50436-6_7","type":"book-chapter","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T19:03:44Z","timestamp":1592593424000},"page":"88-101","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["deal.II Implementation of a Two-Field Finite Element Solver for Poroelasticity"],"prefix":"10.1007","author":[{"given":"Zhuoran","family":"Wang","sequence":"first","affiliation":[]},{"given":"Jiangguo","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"7_CR1","doi-asserted-by":"publisher","first-page":"3332","DOI":"10.1137\/15M1013705","volume":"54","author":"T Arbogast","year":"2016","unstructured":"Arbogast, T., Correa, M.: Two families of mixed finite elements on quadrilaterals of minimal dimension. SIAM J. Numer. Anal. 54, 3332\u20133356 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"7_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-018-0998-7","volume":"142","author":"T Arbogast","year":"2019","unstructured":"Arbogast, T., Tao, Z.: Construction of H(div)-conforming mixed finite elements on cuboidal hexahedra. Numer. Math. 142, 1\u201332 (2019)","journal-title":"Numer. Math."},{"key":"7_CR3","doi-asserted-by":"publisher","unstructured":"Arndt, D., et al.: The deal.II library, version 9.1. J. Numer. Math. (2019). https:\/\/doi.org\/10.1515\/jnma-2019-0064. https:\/\/dealii.org\/deal91-preprint.pdf","DOI":"10.1515\/jnma-2019-0064"},{"key":"7_CR4","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1002\/fld.562","volume":"42","author":"P Bastian","year":"2003","unstructured":"Bastian, P., Riviere, B.: Superconvergence and $$ H(div) $$ projection for discontinuous Galerkin methods. Int. J. Numer. Meth. Fluids 42, 1043\u20131057 (2003)","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"7_CR5","doi-asserted-by":"publisher","first-page":"A2222","DOI":"10.1137\/15M1009822","volume":"37","author":"L Berger","year":"2015","unstructured":"Berger, L., Bordas, R., Kay, D., Tavener, S.: Stabilized lowest-order finite element approximation for linear three-field poroelasticity. SIAM J. Sci. Comput. 37, A2222\u2013A2245 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics","author":"S Brenner","year":"2008","unstructured":"Brenner, S., Scott, L.: The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, vol. 15, 3rd edn. Springer, New York (2008)","edition":"3"},{"key":"7_CR7","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1090\/S0025-5718-1992-1140646-2","volume":"59","author":"S Brenner","year":"1992","unstructured":"Brenner, S., Sung, L.Y.: Linear finite element methods for planar linear elasticity. Math. Comput. 59, 321\u2013338 (1992)","journal-title":"Math. Comput."},{"key":"7_CR8","doi-asserted-by":"publisher","first-page":"A2953","DOI":"10.1137\/120900393","volume":"35","author":"L Bush","year":"2013","unstructured":"Bush, L., Ginting, V.: On the application of the continuous Galerkin finite element method for conservation problems. SIAM J. Sci. Comput. 35, A2953\u2013A2975 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR9","first-page":"357","volume":"16","author":"X Cheng","year":"1998","unstructured":"Cheng, X., Huang, H., Zou, J.: Quadrilateral finite elements for planar linear elasticity problem with large Lam\u00e9 constant. J. Comput. Math. 16, 357\u2013366 (1998)","journal-title":"J. Comput. Math."},{"key":"7_CR10","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1137\/060666305","volume":"45","author":"B Cockburn","year":"2007","unstructured":"Cockburn, B., Gopalakrishnan, J., Wang, H.: Locally conservative fluxes for the continuous Galerkin method. SIAM J. Numer. Anal. 45, 1742\u20131770 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"7_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods","author":"F Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991). https:\/\/doi.org\/10.1007\/978-1-4612-3172-1"},{"key":"7_CR12","doi-asserted-by":"publisher","first-page":"1507","DOI":"10.1002\/nag.1062","volume":"36","author":"J Haga","year":"2012","unstructured":"Haga, J., Osnes, H., Langtangen, H.: On the causes of pressure oscillations in low permeable and low compressible porous media. Int. J. Numer. Anal. Meth. Geomech. 36, 1507\u20131522 (2012)","journal-title":"Int. J. Numer. Anal. Meth. Geomech."},{"key":"7_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/978-3-319-93713-7_6","volume-title":"Computational Science \u2013 ICCS 2018","author":"G Harper","year":"2018","unstructured":"Harper, G., Liu, J., Tavener, S., Wang, Z.: A two-field finite element solver for poroelasticity on quadrilateral meshes. In: Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V.V., Lees, M.H., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2018. LNCS, vol. 10862, pp. 76\u201388. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-93713-7_6"},{"key":"7_CR14","doi-asserted-by":"publisher","first-page":"1917","DOI":"10.1007\/s10915-018-0837-0","volume":"78","author":"G Harper","year":"2019","unstructured":"Harper, G., Liu, J., Tavener, S., Zheng, B.: Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes. J. Sci. Comput. 78, 1917\u20131941 (2019)","journal-title":"J. Sci. Comput."},{"key":"7_CR15","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1016\/j.procs.2017.05.148","volume":"108C","author":"G Harper","year":"2017","unstructured":"Harper, G., Liu, J., Zheng, B.: The THex algorithm and a simple Darcy solver on hexahedral meshes. Proc. Comput. Sci. 108C, 1903\u20131912 (2017)","journal-title":"Proc. Comput. Sci."},{"key":"7_CR16","doi-asserted-by":"crossref","unstructured":"Harper, G., Wang, R., Liu, J., Tavener, S., Zhang, R.: A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements. Technical report, Colorado State University (2020)","DOI":"10.1016\/j.camwa.2020.07.014"},{"key":"7_CR17","doi-asserted-by":"publisher","first-page":"2017","DOI":"10.1016\/j.camwa.2017.07.013","volume":"75","author":"X Hu","year":"2018","unstructured":"Hu, X., Mu, L., Ye, X.: Weak Galerkin method for the Biot\u2019s consolidation model. Comput. Math. Appl. 75, 2017\u20132030 (2018)","journal-title":"Comput. Math. Appl."},{"key":"7_CR18","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1016\/j.jcp.2014.07.001","volume":"276","author":"G Lin","year":"2014","unstructured":"Lin, G., Liu, J., Mu, L., Ye, X.: Weak Galerkin finite element methdos for Darcy flow: anistropy and heterogeneity. J. Comput. Phys. 276, 422\u2013437 (2014)","journal-title":"J. Comput. Phys."},{"key":"7_CR19","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1016\/j.procs.2016.05.485","volume":"80","author":"J Liu","year":"2016","unstructured":"Liu, J., Sadre-Marandi, F., Wang, Z.: Darcylite: a matlab toolbox for Darcy flow computation. Proc. Comput. Sci. 80, 1301\u20131312 (2016)","journal-title":"Proc. Comput. Sci."},{"key":"7_CR20","doi-asserted-by":"publisher","first-page":"B1229","DOI":"10.1137\/17M1145677","volume":"40","author":"J Liu","year":"2018","unstructured":"Liu, J., Tavener, S., Wang, Z.: Lowest-order weak Galerkin finite element method for Darcy flow on convex polygonal meshes. SIAM J. Sci. Comput. 40, B1229\u2013B1252 (2018)","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR21","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.jcp.2018.01.001","volume":"359","author":"J Liu","year":"2018","unstructured":"Liu, J., Tavener, S., Wang, Z.: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes. J. Comput. Phys. 359, 312\u2013330 (2018)","journal-title":"J. Comput. Phys."},{"key":"7_CR22","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0045-7825(78)90005-1","volume":"15","author":"DS Malkus","year":"1978","unstructured":"Malkus, D.S., Hughes, T.: Mixed finite element methods - reduced and selective integration techniques: a unification of concepts. Comput. Meth. Appl. Mech. Eng. 15, 63\u201381 (1978)","journal-title":"Comput. Meth. Appl. Mech. Eng."},{"key":"7_CR23","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.cam.2015.02.001","volume":"285","author":"L Mu","year":"2015","unstructured":"Mu, L., Wang, J., Ye, X.: A weak Galerkin finite element method with polynomial reduction. J. Comput. Appl. Math. 285, 45\u201358 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"7_CR24","first-page":"31","volume":"12","author":"L Mu","year":"2015","unstructured":"Mu, L., Wang, J., Ye, X.: Weak Galerkin finite element methods on polytopal meshes. Int. J. Numer. Anal. Model. 12, 31\u201353 (2015)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"7_CR25","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s10596-007-9045-y","volume":"11","author":"P Phillips","year":"2007","unstructured":"Phillips, P., Wheeler, M.: A coupling of mixed with continuous Galerkin finite element methods for poroelasticity I: the continuous in time case. Comput. Geosci. 11, 131\u2013144 (2007)","journal-title":"Comput. Geosci."},{"key":"7_CR26","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s10596-007-9044-z","volume":"11","author":"P Phillips","year":"2007","unstructured":"Phillips, P., Wheeler, M.: A coupling of mixed with continuous Galerkin finite element methods for poroelasticity II: the-discrete-in-time case. Comput. Geosci. 11, 145\u2013158 (2007)","journal-title":"Comput. Geosci."},{"key":"7_CR27","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s10596-008-9082-1","volume":"12","author":"P Phillips","year":"2008","unstructured":"Phillips, P., Wheeler, M.: A coupling of mixed with discontinuous Galerkin finite element methods for poroelasticity. Comput. Geosci. 12, 417\u2013435 (2008)","journal-title":"Comput. Geosci."},{"key":"7_CR28","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10596-008-9114-x","volume":"13","author":"PJ Phillips","year":"2009","unstructured":"Phillips, P.J., Wheeler, M.F.: Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach. Comput. Geosci. 13, 5\u201312 (2009)","journal-title":"Comput. Geosci."},{"key":"7_CR29","doi-asserted-by":"publisher","first-page":"2528","DOI":"10.1137\/080722953","volume":"31","author":"S Sun","year":"2009","unstructured":"Sun, S., Liu, J.: A locally conservative finite element method based on piecewise constant enrichment of the continuous Galerkin method. SIAM J. Sci. Comput. 31, 2528\u20132548 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"7_CR30","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.cam.2015.12.015","volume":"307","author":"C Wang","year":"2016","unstructured":"Wang, C., Wang, J., Wang, R., Zhang, R.: A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation. J. Comput. Appl. Math. 307, 346\u2013366 (2016)","journal-title":"J. Comput. Appl. Math."},{"key":"7_CR31","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.cam.2012.10.003","volume":"241","author":"J Wang","year":"2013","unstructured":"Wang, J., Ye, X.: A weak Galerkin finite element method for second order elliptic problems. J. Comput. Appl. Math. 241, 103\u2013115 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"7_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/978-3-030-22747-0_37","volume-title":"Computational Science \u2013 ICCS 2019","author":"Z Wang","year":"2019","unstructured":"Wang, Z., Harper, G., O\u2019Leary, P., Liu, J., Tavener, S.: deal.II implementation of a weak galerkin finite element solver for Darcy flow. In: Rodrigues, J.M.F., et al. (eds.) ICCS 2019. LNCS, vol. 11539, pp. 495\u2013509. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-22747-0_37"},{"key":"7_CR33","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10596-013-9382-y","volume":"18","author":"M Wheeler","year":"2014","unstructured":"Wheeler, M., Xue, G., Yotov, I.: Coupling multipoint flux mixed finite element methods with continuous Galerkin methods for poroelasticity. Comput. Geosci. 18, 57\u201375 (2014)","journal-title":"Comput. Geosci."},{"key":"7_CR34","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1002\/num.21775","volume":"29","author":"SY Yi","year":"2013","unstructured":"Yi, S.Y.: A coupling of nonconforming and mixed finite element methods for Biot\u2019s consolidation model. Numer. Meth. PDEs 29, 1749\u20131777 (2013)","journal-title":"Numer. Meth. PDEs"},{"key":"7_CR35","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1002\/num.21865","volume":"30","author":"SY Yi","year":"2014","unstructured":"Yi, S.Y.: Convergence analysis of a new mixed finite element method for Biot\u2019s consolidation model. Numer. Meth. PDEs 30, 1189\u20131210 (2014)","journal-title":"Numer. Meth. PDEs"},{"key":"7_CR36","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1137\/16M1056109","volume":"55","author":"SY Yi","year":"2017","unstructured":"Yi, S.Y.: A study of two modes of locking in poroelasticity. SIAM J. Numer. Anal. 55, 1915\u20131936 (2017)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-50436-6_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T23:03:07Z","timestamp":1718751787000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-50436-6_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030504359","9783030504366"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-50436-6_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"15 June 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Amsterdam","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 June 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 June 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2020\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"230","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"98","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"43% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.5","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"248 workshop papers were selected from 489 submissions to the thematic tracks. The conference was canceled due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}