An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation
Mathematics of Computation
A posteriori error estimation for variational problems with uniformly convex functionals
Mathematics of Computation
Fully Reliable Localized Error Control in the FEM
SIAM Journal on Scientific Computing
Convex analysis and variational problems
Convex analysis and variational problems
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
A new a posteriori error estimate for convection-reaction-diffusion problems
Journal of Computational and Applied Mathematics
Certified error bounds for uncertain elliptic equations
Journal of Computational and Applied Mathematics
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The present work is devoted to the a posteriori error estimation for 2nd order elliptic problems with Dirichlet boundary conditions. Using the duality technique we derive the reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1. independently of the discretization method chosen. In particular, our error estimator can be applied also to problems and discretizations where the Galerkin orthogonality is not available. We will present different strategies for the evaluation of the error estimator. Only one constant appears in its definition which is the one from Friedrichs' inequality; that constant depends solely on the domain geometry, and the estimator is quite non-sensitive to the error in the constant evaluation. Finally, we show how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.