An equilibrated a posteriori error estimator for an interior penalty discontinuous Galerkin approximation of the \(p\)-Laplace problem. (English) Zbl 1481.65227
The paper deals with the numerical solution of \(p\)-Laplace equation (\(p>1\)) by the interior penalty discontinuous Galerkin method. The equilibrated a posteriori error estimator are derived and the upper bound for the discretization error in the broken \(W^{1,p}\)-norm are proved. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results for a \(L\)-shaped domain illustrate the performance of both estimators.
Reviewer: Vit Dolejsi (Praha)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
Keywords:
interior penalty discontinuous Galerkin method; \(p\)-Laplace problem; a posteriori error estimation; equilibrationReferences:
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