A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem
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Thirupathi Gudi
und
Kamana Porwal
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.
Funding source: DST Fast Track Project
Funding source: UGC Center for Advanced Study
Funding source: Council for Scientific and Industrial Research (CSIR)
The authors would like to acknowledge the fruitful discussions with Professor Carsten Carstensen and Professor Andreas Veeser.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations
- Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems
- A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem
- On the Theory of TE Waves Guided by a Lossy Three-Layer Structure with General Nonlinear Permittivity
- Analysis of Model Variance for Ensemble Based Turbulence Modeling
- On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators
- Approximation of Semilinear Fractional Cauchy Problem
- Pointwise Computation in an Ill-Posed Spherical Pseudo-Differential Equation
- On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers
- The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrödinger Equation
Artikel in diesem Heft
- Frontmatter
- Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations
- Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems
- A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem
- On the Theory of TE Waves Guided by a Lossy Three-Layer Structure with General Nonlinear Permittivity
- Analysis of Model Variance for Ensemble Based Turbulence Modeling
- On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators
- Approximation of Semilinear Fractional Cauchy Problem
- Pointwise Computation in an Ill-Posed Spherical Pseudo-Differential Equation
- On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers
- The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrödinger Equation
