LEADER 04225nam 22005775 450 001 9910300130603321 005 20200704090717.0 010 $a3-319-79042-0 024 7 $a10.1007/978-3-319-79042-8 035 $a(CKB)4100000005323572 035 $a(DE-He213)978-3-319-79042-8 035 $a(MiAaPQ)EBC6315562 035 $a(PPN)229503063 035 $a(EXLCZ)994100000005323572 100 $a20180731d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Gradient Discretisation Method /$fby Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIV, 497 p. 33 illus., 14 illus. in color.) 225 1 $aMathématiques et Applications,$x1154-483X ;$v82 311 $a3-319-79041-2 320 $aIncludes bibliographical references and index. 327 $aPart I Elliptic problems -- Part II Parabolic problems -- Part III Examples of gradient discretisation methods -- Part IV Appendix. 330 $aThis monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray?Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.