04225nam 22005775 450 991030013060332120200704090717.03-319-79042-010.1007/978-3-319-79042-8(CKB)4100000005323572(DE-He213)978-3-319-79042-8(MiAaPQ)EBC6315562(PPN)229503063(EXLCZ)99410000000532357220180731d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe Gradient Discretisation Method /by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XXIV, 497 p. 33 illus., 14 illus. in color.) Mathématiques et Applications,1154-483X ;823-319-79041-2 Includes bibliographical references and index.Part I Elliptic problems -- Part II Parabolic problems -- Part III Examples of gradient discretisation methods -- Part IV Appendix.This 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.<span style="font-family:" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.<span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations.Mathématiques et Applications,1154-483X ;82Computer scienceMathematicsDifferential equations, PartialComputational Mathematics and Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M1400XPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Computer scienceMathematics.Differential equations, Partial.Computational Mathematics and Numerical Analysis.Partial Differential Equations.518.63Droniou Jérômeauthttp://id.loc.gov/vocabulary/relators/aut941783Eymard Robertauthttp://id.loc.gov/vocabulary/relators/autGallouët Thierryauthttp://id.loc.gov/vocabulary/relators/autGuichard Cindyauthttp://id.loc.gov/vocabulary/relators/autHerbin Raphaèleauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300130603321The Gradient Discretisation Method2124843UNINA