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Defect Correction for Operator Equations
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a-posteriori error estimates accuracy adaptive algorithm Anal analysis application approximate inverse approximate solution assume assumptions asymptotic analysis asymptotic expansions B-convergence Banach space Bohmer boundary conditions boundary value problems Comp computation consider convergence corresponding defect correction defect correction method defect correction principle defect correction step defined denotes Dirichlet Dirichlet boundary conditions Discrete Newton methods discretization error discretization methods elliptic example finite element method fixed point Frechet-derivatives function given global discretization error global error Hackbusch Hemker IDeC IDeC-algorithms initial approximation interpolation interval invariant subspace iterated defect corrections iteration step Lemma linear equations linear systems mapping Math Mathematics matrix MDCP mesh model problem multigrid iteration multigrid method Newton's method norm numerical solution obtained ordinary differential equations Pereyra polynomial Proof relaxation residual satisfies Section sequence SIAM singular perturbation small parameter smooth solved Stetter subintervals Theorem Ueberhuber vector