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Abstract : |
Abstract. The solution of the large linear systems arising from finite element discretizations of elliptic boundary value problems is a basic task in numerical analysis. For uniformly refined grids, multigrid methods are well established and very efficient methods to solve these problems. For adaptively generated, strongly nonuniform grids, the situation is more complicated, both with regard to convergence properties and with regard to the computational complexity of the single iteration step. The paper discusses a surprisingly simple approach which is very well suited to nonuniform grids, the hierarchical decomposition of finite element spaces. The method is based on an old idea from the theory of real functions, which is often used to produce fractal curves and surfaces. It is closely related to recent L 2--like decompositions., |
