The Gradient Discretisation Method

August 11, 2018|
The Gradient Discretisation Method by J Droniou
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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=" 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.

Jérôme Droniou is Associate Professor at Monash University, Australia. His research focuses on elliptic and parabolic PDEs. He has published many papers on theoretical and numerical analysis of models with singularities or degeneracies, including convergence analysis of schemes without regularity assumptions on the data or so...
Title:The Gradient Discretisation Method
Product dimensions:497 pages, 9.25 X 6.1 X 0 in
Shipping dimensions:497 pages, 9.25 X 6.1 X 0 in
Published:August 11, 2018
Publisher:Springer Nature
Appropriate for ages:All ages
ISBN - 13:9783319790411

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