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

International Journal of Applied Mathematics and Computer Science (2013)

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

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topHani 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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