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" Algorithms and Theory in Filtering and Control "
edited by Danny C. Sorensen, Roger J. -B. Wets.
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BL
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| Record Number
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865859
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| Title & Author
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The gradient discretisation method /\ Jérôme Droniou [and others].
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| Publication Statement
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Cham :: Springer,, 2018.
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| Series Statement
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Mathématiques et applications ;; 82
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| Page. NO
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1 online resource
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| ISBN
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3319790420
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: 9783319790428
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3319790412
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9783319790411
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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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| Abstract
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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.
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| Subject
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Discretization (Mathematics)
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| Subject
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Differential calculus equations.
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