Adaptive Frame Algorithms for Elliptic Operator Equations

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...

Adaptive frame methods for elliptic operator equations: the steepest descent approach

This paper is concerned with the development of adaptive numerical methods for elliptic operator equations. We are particularly interested in discretization schemes based on wavelet frames. We show that by using three basic subroutines an implementable, convergent scheme can be derived, which, moreover, has optimal computational complexity. The scheme is based on adaptive steepest descent itera...

Adaptive Wavelet Algorithms for solving operator equations

Adaptive Wavelet and Frame Schemes for Elliptic and Parabolic Equations

Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften v Acknowledgements I would like to sincerely thank my research advisor, Professor Stephan Dahlke, whose guidance, patience and constant willingness for discussions about wavelet and frame analysis substantially helped me to finish this thesis. I am also indebted to Professor Hans–Jürgen Reinhardt for being my second referee and...

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...