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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 15, Issue 4


An Adaptive Wavelet Method for Semi-Linear First-Order System Least Squares

Nabi Chegini / Rob Stevenson
  • Corresponding author
  • Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
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Published Online: 2015-08-27 | DOI: https://doi.org/10.1515/cmam-2015-0023


We design an adaptive wavelet scheme for solving first-order system least-squares formulations of second-order elliptic PDEs that converge with the best possible rate in linear complexity. A wavelet Riesz basis is constructed for the space H0,ΓN(div;Ω) on general polygons. The theoretical findings are illustrated by numerical experiments.

Keywords: Adaptive Wavelet Methods; Least Squares Formulations of Boundary Value Problems; Optimal Convergence Rates; Linear Complexity

MSC: 41A25; 42C40; 47J25; 65J15; 65N12; 65T60; 65N30

About the article

Received: 2015-02-11

Revised: 2015-08-07

Accepted: 2015-08-10

Published Online: 2015-08-27

Published in Print: 2015-10-01

Citation Information: Computational Methods in Applied Mathematics, Volume 15, Issue 4, Pages 439–463, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0023.

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