Gradient discretisation method
Gradient discretisation method
- Cham : Springer, 2018.
- xxiv, 497 pages : 19 b/w illustrations, 14 illustrations in colour
- Mathématiques et applications, 82 1154-483X ; .
Includes bibliographical references and index
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.
9783319790411
Discretization (Mathematics)
Computer mathematics
Elliptic partial differential equations
Gradient discretisation method
Parabolic partial differential equations
Gradient schemes
Discrete Aubin-Simon compactness theorems
519.6 / DRO-G
Includes bibliographical references and index
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.
9783319790411
Discretization (Mathematics)
Computer mathematics
Elliptic partial differential equations
Gradient discretisation method
Parabolic partial differential equations
Gradient schemes
Discrete Aubin-Simon compactness theorems
519.6 / DRO-G
