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

Hani Akbari

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 17-27
  • ISSN: 1641-876X

Abstract

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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 H 1 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.

How to cite

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Hani Akbari. "Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 17-27. <http://eudml.org/doc/275849>.

@article{HaniAkbari2013,
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 H 1 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.},
author = {Hani Akbari},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {general stationary elliptic BVPs; Robin boundary condition; orthogonal Coifman wavelets; trivariate connection coefficients; fast convergence; general stationary elliptic boundary value problems; Galerkin method; numerical experiment},
language = {eng},
number = {1},
pages = {17-27},
title = {Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs},
url = {http://eudml.org/doc/275849},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Hani Akbari
TI - Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 17
EP - 27
AB - 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 H 1 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.
LA - eng
KW - general stationary elliptic BVPs; Robin boundary condition; orthogonal Coifman wavelets; trivariate connection coefficients; fast convergence; general stationary elliptic boundary value problems; Galerkin method; numerical experiment
UR - http://eudml.org/doc/275849
ER -

References

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