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An algorithm for coarsening unstructured meshes. (English) Zbl 0857.65034

From the authors’ abstract: We develop and analyze a procedure for creating a hierarchical basis of continuous piecewise linear polynomials on an arbitrary, unstructured, nonuniform triangular mesh. Using these hierarchical basis functions, we are able to define and analyze corresponding iterative methods for solving the linear systems arising from finite element discretizations of elliptic partial differential equations. In particular, we show that the generalized condition numbers for such iterative methods are of order \(J^2\), where \(J\) is the number of hierarchical basis levels.
Reviewer: Th.Sonar (Hamburg)

MSC:

65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
65F35 Numerical computation of matrix norms, conditioning, scaling
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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