Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments

Authors:
Arne Barinka;Titus Barsch;Philippe Charton;Albert Cohen;Stephan Dahlke;Wolfgang Dahmen;Karsten Urban
Affiliations:
-;-;-;-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2001

Citing 0
Cited 8

Fast Iterative Solution of Saddle Point Problems in Optimal Control Based on Wavelets

Computational Optimization and Applications
Adaptive biorthogonal spline schemes for advection-reaction equations

Journal of Computational Physics
An adaptive multilevel wavelet collocation method for elliptic problems

Journal of Computational Physics
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations

Journal of Computational Physics
Adaptive multiresolution finite element method based on second generation wavelets

Finite Elements in Analysis and Design
Optimal adaptive computations in the Jaffard algebra and localized frames

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Space-Time Adaptive Wavelet Methods for Optimal Control Problems Constrained by Parabolic Evolution Equations

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Efficient application of nonlinear stationary operators in adaptive wavelet methods--the isotropic case

Numerical Algorithms

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Abstract

Recently an adaptive wavelet scheme could be proved to be asymptotically optimal for a wide class of elliptic operator equations in the sense that the error achieved by an adaptive approximate solution behaves asymptotically like the smallest possible error that can be realized by any linear combination of the corresponding number of wavelets. On one hand, the results are purely asymptotic. On the other hand, the analysis suggests new algorithmic ingredients for which no prototypes seem to exist yet. It is therefore the objective of this paper to develop suitable data structures for the new algorithmic components and to obtain a quantitative validation of the theoretical results. We briefly review first the main theoretical facts, describe the main ingredients of the algorithm, highlight the essential data structures, and illustrate the results by one- and two-dimensional numerical examples including comparisons with an adaptive finite element scheme.