<abstract xmlns="http://www.w3.org/1999/xhtml">We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2 −nN ) in the H1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection coefficients. Due to the fast convergence rate, very good approximations are found at low levels and with low Coiflet degrees, hence the size of corresponding linear systems is small. Numerical experiments confirm these claims.</abstract>

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2 −nN ) in the H1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection coefficients. Due to the fast convergence rate, very good approximations are found at low levels and with low Coiflet degrees, hence the size of corresponding linear systems is small. Numerical experiments confirm these claims.

Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

Department of Applied Mathematics Ferdowsi University of Mashhad, Mashhad, Iran

International Journal of Applied Mathematics and Computer Science

{"article-title":"Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs"}

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove...

Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

Pubblicato online: 26 mar 2013

Pagine: 17 - 27

DOI: https://doi.org/10.2478/amcs-2013-0002

This content is open access.