Implicit a posteriori error estimation using patch recovery techniques


Horváth, Tamás L. and Izsák, Ferenc (2012) Implicit a posteriori error estimation using patch recovery techniques. Central European Journal of Mathematics, 10 (1). pp. 55-72. ISSN 1644-3616

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Abstract:We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
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Copyright:© 2012 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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