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Interior layer: Discrete solution and corresponding polynomial degrees
We consider the h-p finite element method for elliptic problems in one dimension. A mathematical derivation of a posteriori estimates for the error and the error reduction corresponding to an h- or p-refinement of elements is presented. The estimation of the error reduction is based on the solution of local problems. For the model problem $-u'' = f$ these estimates are valid on single elements.
Based on these a posteriori estimates an adaptive algorithm is derived. Numerical results show the efficiency of the estimators for several problem classes. For the $x^\alpha$ model singularity the a priori known optimal h-p mesh is obtained by this algorithm.
Applied Numerical Mathematics 35 (2000), 43-66.
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