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Record Nr. |
UNINA9910300130603321 |
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Autore |
Droniou Jérôme |
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Titolo |
The Gradient Discretisation Method [[electronic resource] /] / by Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
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ISBN |
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Edizione |
[1st ed. 2018.] |
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Descrizione fisica |
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1 online resource (XXIV, 497 p. 33 illus., 14 illus. in color.) |
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Collana |
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Mathématiques et Applications, , 1154-483X ; ; 82 |
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Disciplina |
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Soggetti |
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Computer mathematics |
Partial differential equations |
Computational Mathematics and Numerical Analysis |
Partial Differential Equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Part I Elliptic problems -- Part II Parabolic problems -- Part III Examples of gradient discretisation methods -- Part IV Appendix. |
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Sommario/riassunto |
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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="" |
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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. |
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