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The Gradient Discretisation Method

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Gradient Discretisation Method/ by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin.
作者:	Droniou, Jérôme.
其他作者:	Eymard, Robert.
面頁冊數:	XXIV, 497 p. 33 illus., 14 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Computer mathematics. -
電子資源:	https://doi.org/10.1007/978-3-319-79042-8
ISBN:	9783319790428

The Gradient Discretisation Method
Droniou, Jérôme.

The Gradient Discretisation Method[electronic resource] /by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin. - 1st ed. 2018. - XXIV, 497 p. 33 illus., 14 illus. in color.online resource. - Mathématiques et Applications,821154-483X ;. - Mathématiques et Applications,76.

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.

ISBN: 9783319790428

Standard No.: 10.1007/978-3-319-79042-8doiSubjects--Topical Terms:

1199796
Computer mathematics.

LC Class. No.: QA71-90

Dewey Class. No.: 518

The Gradient Discretisation Method
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