Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs

DOI10.1007/s10915-012-9644-1zbMath1279.65132OpenAlexW2027046761MaRDI QIDQ356786

Scott Congreve, Thomas P. Wihler, Paul Houston

Publication date: 26 July 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-012-9644-1

zbMATH Keywords

numerical experimentsadaptivitydiscontinuous Galerkin methods\(hp\)-finite element methodsquasilinear PDEs, error boundssecond-order quasilinear elliptic boundary-value problemtwo-grid methods

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Quasilinear elliptic equations (35J62)

Related Items (14)

An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems ⋮ Two-grid \textit{hp}-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes ⋮ Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs ⋮ A Two-Grid Block-Centered Finite Difference Method For Darcy--Forchheimer Flow in Porous Media ⋮ A two-grid method for discontinuous Galerkin approximations to compressible miscible displacement problems ⋮ Unnamed Item ⋮ A posteriori error estimates of two-grid weak Galerkin methods for semilinear elliptic differential equations ⋮ Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem ⋮ Two-grid IPDG discretization scheme for nonlinear elliptic PDEs ⋮ Adaptive energy minimisation for \(hp\)-finite element methods ⋮ A two-grid discontinuous Galerkin method for a kind of nonlinear parabolic problems ⋮ An \(hp\)-adaptive iterative linearization discontinuous-Galerkin FEM for quasilinear elliptic boundary value problems ⋮ Analysis of Adaptive Two-Grid Finite Element Algorithms for Linear and Nonlinear Problems ⋮ Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium

Uses Software

• MUMPS

Cites Work

• Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs
• Two-grid discontinuous Galerkin method for quasi-linear elliptic problems
• An \(hp\)-adaptive strategy based on continuous Sobolev embeddings
• Nonobtuse tetrahedral partitions that refine locally towards Fichera-like corners.
• Multifrontal parallel distributed symmetric and unsymmetric solvers
• A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
• Exponential convergence of the \(hp\)-DGFEM for diffusion problems
• Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
• Two-grid finite volume element method for linear and nonlinear elliptic problems
• \(hp\)-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems
• ENERGY NORM A POSTERIORI ERROR ESTIMATION FOR hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS IN THREE DIMENSIONS
• ℎ𝑝-Optimal discontinuous Galerkin methods for linear elliptic problems
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs
• Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems
• Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems
• A Novel Two-Grid Method for Semilinear Elliptic Equations
• Two-grid finite element formulations of the incompressible Navier-Stokes equations
• A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• A Two-Level Method for the Discretization of Nonlinear Boundary Value Problems
• Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs