Adaptive wavelet methods for elliptic operator equations: Convergence rates

Adaptive wavelet methods for elliptic operator equations: Convergence rates

This paper is concerned with the construction and analysis of wavelet-based adaptive algorithms for the numerical solution of elliptic equations. These algorithms approximate the solution u of the equation by a linear combination of N wavelets. Therefore, a benchmark for their performance is provided by the rate of best approximation to u by an arbitrary linear combination of N wavelets (so cal...

Adaptive Wavelet Methods for Elliptic Operator Equations with Nonlinear Terms

We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategie...

Adaptive frame methods for elliptic operator equations

Stephan Dahlke a, Massimo Fornasier b and Thorsten Raasch a a Philipps-Universität Marburg, FB 12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032 Marburg, Germany E-mail: {dahlke;raasch}@mathematik.uni-marburg.de b Università “La Sapienza” in Roma, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via Antonio Scarpa, 16/B, 00161 Roma, Italy E-mail: mfornasi...

An optimal adaptive wavelet method - for strongly elliptic operator equations

Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations Multiscale Wavelet Methods for Pdes

w I n t r o d u c t i o n Adaptive methods are an important tool for numerically solving elliptic equations. Their origins appear in the adaptive grid refinements in finite element methods. Heuristically, adaptive methods are effective when trying to recover solutions u which exhibit singularities. Much impetus to the theory of adaptive finite element methods was provided by the introduction M ...