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＜E-Book＞
The Gradient Discretisation Method / by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin
(Mathématiques et Applications. ISSN:21983275 ; 82)

Edition	1st ed. 2018.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2018
Language	English
Size	XXIV, 497 p. 33 illus., 14 illus. in color : online resource
Authors	*Droniou, Jérôme author Eymard, Robert author Gallouët, Thierry author Guichard, Cindy author Herbin, Raphaèle author SpringerLink (Online service)
Subjects	LCSH:Mathematics -- Data processing  All Subject Search LCSH:Differential equations FREE:Computational Mathematics and Numerical Analysis FREE:Differential Equations
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-79042-8

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