Hierarchical bases for elliptic problems

Dörfler, W.

doi:10.1090/S0025-5718-1992-1122064-6

Hierarchical bases for elliptic problems
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Math. Comp. 58 (1992), 513-529 Request permission

Abstract:

Linear systems of equations with positive and symmetric matrices often occur in the numerical treatment of linear and nonlinear elliptic boundary value problems. If the CG algorithm is used to solve these equations, one is able to speed up the convergence by "preconditioning." The method of preconditioning with hierarchical basis has already been considered for the Laplace equation in two space dimensions and for linear conforming elements. In the present work this method is generalized to a large class of conforming and nonconforming elements.

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