{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T04:13:30Z","timestamp":1751516010505,"version":"3.41.0"},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The Biot problem of poroelasticity is extended by Signorini contact conditions. The resulting Biot contact problem is formulated and analyzed as a two field variational inequality problem of a perturbed saddle point structure. We present an a priori error analysis for a general as well as for an <jats:italic>hp<\/jats:italic>-FE discretization including convergence and guaranteed convergence rates for the latter. In particular, these rates are always optimal in the discretization parameters for the fluid pressure, and can be linear for the lowest order <jats:italic>h<\/jats:italic>-version. Moreover, we state a residual based a posteriori error estimator.\nNumerical results underline our theoretical findings and show that optimal, in particular exponential, convergence rates can be achieved by adaptive schemes for two-dimensional problems.<\/jats:p>","DOI":"10.1515\/cmam-2025-0012","type":"journal-article","created":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T16:59:08Z","timestamp":1751475548000},"page":"529-545","source":"Crossref","is-referenced-by-count":0,"title":["Contact Problems in Porous Media"],"prefix":"10.1515","volume":"25","author":[{"given":"Lothar","family":"Banz","sequence":"first","affiliation":[{"name":"Department of Mathematics , University of Salzburg , Salzburg , Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fleurianne","family":"Bertrand","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics , 38869 TU Chemnitz , Chemnitz , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"2025070217063901508_j_cmam-2025-0012_ref_001","doi-asserted-by":"crossref","unstructured":"L.  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Stephan,\nHigher order mixed FEM for the obstacle problem of the p-Laplace equation using biorthogonal systems,\nComput. Methods Appl. Math. 19 (2019), no. 2, 169\u2013188.","DOI":"10.1515\/cmam-2018-0015"},{"key":"2025070217063901508_j_cmam-2025-0012_ref_005","doi-asserted-by":"crossref","unstructured":"L.  Banz, J.  Petsche and A.  Schr\u00f6der,\nHybridization and stabilization for hp-finite element methods,\nAppl. Numer. Math. 136 (2019), 66\u2013102.","DOI":"10.1016\/j.apnum.2018.09.017"},{"key":"2025070217063901508_j_cmam-2025-0012_ref_006","doi-asserted-by":"crossref","unstructured":"L.  Banz and A.  Schr\u00f6der,\nBiorthogonal basis functions in hp-adaptive FEM for elliptic obstacle problems,\nComput. Math. Appl. 70 (2015), no. 8, 1721\u20131742.","DOI":"10.1016\/j.camwa.2015.07.010"},{"key":"2025070217063901508_j_cmam-2025-0012_ref_007","doi-asserted-by":"crossref","unstructured":"L.  Banz and E. P.  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