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Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch of the optimal complexity of this algorithm with respect to an approximation class of solutions. As in the last chapter the relations between the strong and weak form of the equations are the key for deriving upper and lower a posteriori error estimates. Quantities of interest are estimated.
Keywords: a posteriori error estimation; adaptive mesh refinement; algorithm; convergence; optimal complexity; quantities of interest
Chapter. 8839 words. Illustrated.
Subjects: Mathematical and Statistical Physics
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