Hierarchical error estimates for finite volume approximation solution of elliptic equations
Applied Numerical Mathematics
Efficient and reliable hierarchical error estimates for an elliptic obstacle problem
Applied Numerical Mathematics
A Novel Hierarchial Error Estimate for Elliptic Obstacle Problems
Journal of Scientific Computing
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We consider obstacle problems where a quadratic functional associated with the Laplacian is minimized in the set of functions above a possibly discontinuous and thin but piecewise affine obstacle. In order to approximate minimum point and value, we propose an adaptive algorithm that relies on minima with respect to admissible linear finite element functions and on an a posteriori estimator for the error in the minimum value. It is proven that the generated sequence of approximate minima converges to the exact one. Furthermore, our numerical results in two and three dimensions indicate that the convergence rate with respect to the number of degrees of freedom is optimal in that it coincides with the one of nonlinear or adaptive approximation.