The Gradient Discretisation Method / / by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin
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| Autore: |
Droniou Jérôme
|
| Titolo: |
The Gradient Discretisation Method / / by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Edizione: | 1st ed. 2018. |
| Descrizione fisica: | 1 online resource (XXIV, 497 p. 33 illus., 14 illus. in color.) |
| Disciplina: | 518.63 |
| Soggetto topico: | Computer mathematics |
| Partial differential equations | |
| Computational Mathematics and Numerical Analysis | |
| Partial Differential Equations | |
| Persona (resp. second.): | EymardRobert |
| GallouëtThierry | |
| GuichardCindy | |
| HerbinRaphaèle | |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | Part I Elliptic problems -- Part II Parabolic problems -- Part III Examples of gradient discretisation methods -- Part IV Appendix. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | The Gradient Discretisation Method |
| ISBN: | 3-319-79042-0 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910300130603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Mathématiques et Applications, . 1154-483X ; ; 82