Computational Methods in Applied Mathematics · 2015 · 24 citations · 0 references
ComputingComputational EngineeringMathematicsComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsSolid Mechanics ApplicationsA Posteriori AnalysisA Posteriori Error EstimatesA Posteriori Error EstimationA Priori Error AnalysisA Priori Error EstimatesA Priori Error EstimationElement ResidualsError Estimation For Finite Element Solutions
Abstract A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.