Mathematical Models and Methods in Applied Sciences · 2007 · 166 citations · 31 references
ComputingComputational EngineeringComputational Fluid DynamicsFinite Element AnalysisFinite Element MethodsAdaptive Mesh RefinementConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsA Posteriori Error EstimatesA Posteriori Error EstimationAdaptive RefinementElliptic Boundary-value ProblemsEnergy Norm Error AnalysisGalerkin DiscretizationLocal Mesh RefinementLower Bounds
In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments illustrate the performance of the proposed estimators within an automatic hp-adaptive refinement procedure.
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Introduction to Adaptive Methods for Differential Equations
Kenneth Eriksson, D. Estep, Peter Hansbo et al. · Acta Numerica · 1995 · 625 citations