A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

DOI10.1051/m2an/2019022zbMath1448.65211arXiv1807.10645OpenAlexW2883398524MaRDI QIDQ5242222

Assyr Abdulle, Giacomo Rosilho de Souza

Publication date: 6 November 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.10645

zbMATH Keywords

discontinuous Galerkinquasilinear PDEslocal schemegradient discretization

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Nonlinear constitutive equations for materials with memory (74D10) Complexity and performance of numerical algorithms (65Y20) Quasilinear elliptic equations (35J62) Preconditioners for iterative methods (65F08)

Related Items (2)

A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations ⋮ A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Uses Software

• libMesh

Cites Work

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• Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity
• Mathematical aspects of discontinuous Galerkin methods.
• A posteriori estimates for partial differential equations
• A finite volume convergence theory for the fast adaptive composite grid methods
• The gradient discretisation method
• Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form
• Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection
• The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations
• On the poisson equation with intersecting interfaces
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems
• Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems
• A COST/BENEFIT ANALYSIS OF SIMPLICIAL MESH IMPROVEMENT TECHNIQUES AS MEASURED BY SOLUTION EFFICIENCY
• Convergence of Adaptive Finite Element Methods
• A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

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