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A wavelet-based adaptive finite element method for advection-diffusion equations. (English) Zbl 0872.65099
The authors propose a new wavelet-based procedure for adapting the finite element method to structure of the solutions. First the finite element solution is computed on the given mesh, and then it is analyzed by wavelets on a super imposed regular grid. The result of analysis leads to a new adapted distribution of grid points via a Delaunay triangulation. The authors give several examples of discretizations of a convection-diffusion problem which indicate the flexibility of this approach.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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