Adaptive wavelet methods. II: Beyond the elliptic case
[For part I see Math. Comput. 70, 27--75 (2001; Zbl 0980.65130)]. Design and analysis of adaptive wavelet methods for systems of operator equations is presented. The existing theory on adaptive wavelet-based methods is extended from symmetric positive definite problems to indefinite or nonsymmetric systems of operator equations. This is accomplished by introducing techniques (such as the least-squares formulation) that transform the original (continuous problem) into an equivalent infinite system of equations which is now well-posed in the Euclidean metric. For a wide range of problems it is shown that the new adaptive method performs with asymptotically optimal complexity. Furthermore it automatically stabilizes the numerical procedure so that, for instance, compatibility constraints on the choice of spaces, like the Ladyshenskaya-Babuška-Brezzi condition, no longer arise.
scientific article; zbMATH DE number 1890496