Energy norm a posteriori error estimation for \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. (English) Zbl 1220.65156
The authors derive an a posteriori error estimator for \(hp\) adaptive discontinuous Galerkin (DG) methods for elliptic problems on 1-irregularly and isotropically refined, affine hexahedral meshes in three dimensions. The estimator yields upper and lower bounds for the error measured in terms of the natural energy norm. The estimate is applied as an error indicator for an energy norm error estimation in an \(hp\)-adaptive refinement algorithm. The numerical tests show that the indicator is efficient in locating and resolving isotropic corner singularities at exponential convergence rates.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
energy norm; \(hp\) adaptive discontinuous Galerkin methods; elliptic problems; three dimensions; numerical examples; a posteriori error estimator; adaptive refinement algorithm; exponential convergenceReferences:
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