An equilibrated a posteriori error estimator for an interior penalty discontinuous Galerkin approximation of the $p$-Laplace problem

DOI10.1515/rnam-2021-0026zbMath1481.65227OpenAlexW4200627460MaRDI QIDQ825913

Publication date: 18 December 2021

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

Full work available at URL: https://doi.org/10.1515/rnam-2021-0026

zbMATH Keywords

a posteriori error estimation $p$-Laplace problem interior penalty discontinuous Galerkin method equilibration

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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

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An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems
Mathematical aspects of discontinuous Galerkin methods.
An introduction to Sobolev spaces and interpolation spaces
A posteriori estimates for partial differential equations
Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian
Equilibrated residual error estimates are $p$-robust
Convergent adaptive finite elements for the nonlinear Laplacian
Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form
Analysis on an HDG method for the $p$-Laplacian equations
An accurate $\mathbf H$(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems
Contractive projections in $L_ p$-spaces
Quasi-Norm Local Error Estimators forp-Laplacian
A Hybridizable Discontinuous Galerkin Method for the $p$-Laplacian
Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements
Optimality of an adaptive finite element method for the p-Laplacian equation
An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method
Guaranteed and robust error bounds for nonconforming approximations of elliptic problems
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
A posteriori error estimates of functional type for variational problems related to generalized Newtonian fluids
Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems
Equilibrated error estimators for discontinuous Galerkin methods
Linear Convergence of an Adaptive Finite Element Method for the p-Laplacian Equation
Compact embeddings of broken Sobolev spaces and applications
Mixed and Hybrid Finite Element Methods
Finite Element Approximation of the p-Laplacian
A Posteriori Finite Element Error Control for the P-Laplace Problem
A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
On Quasi-Norm Interpolation Error Estimation And A Posteriori Error Estimates for p-Laplacian
A Convergent Adaptive Algorithm for Poisson’s Equation
Interior Penalty Discontinuous Galerkin FEM for the $p(x)$-Laplacian
L^p-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS
A posteriori error estimation for variational problems with uniformly convex functionals
Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method
Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
Finite element quasi-interpolation and best approximation
A two-energies principle for the biharmonic equation and ana posteriorierror estimator for an interior penalty discontinuous Galerkin approximation
Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case
Finite Elements

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An equilibrated a posteriori error estimator for an interior penalty discontinuous Galerkin approximation of the \(p\)-Laplace problem