A numerical scheme based on

mean value solutions for

the helmholtz equation

on triangular grids

Authors:
M. G. Andrade and J. B. R. do Val

Journal:
Math. Comp. **66** (1997), 477-493

MSC (1991):
Primary 35A40, 65N06; Secondary 35J25, 65N15, 65N22

DOI:
https://doi.org/10.1090/S0025-5718-97-00825-9

MathSciNet review:
1401937

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Abstract | References | Similar Articles | Additional Information

Abstract: A numerical treatment for the Dirichlet boundary value problem on regular triangular grids for homogeneous *Helmholtz* equations is presented, which also applies to the convection-diffusion problems. The main characteristic of the method is that an accuracy estimate is provided in analytical form with a better evaluation than that obtained with the usual finite difference method. Besides, this classical method can be seen as a truncated series approximation to the proposed method. The method is developed from the analytical solutions for the Dirichlet problem on a ball together with an error evaluation of an integral on the corresponding circle, yielding accuracy. Some numerical examples are discussed and the results are compared with other methods, with a consistent advantage to the solution obtained here.

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Additional Information

**M. G. Andrade**

Affiliation:
Depto. de Ciencias de Computacao e Estatistica, Instituto de Ciencias Matematica de Sao Carlos, Universidade de Sao Paulo, C.P. 668 - Sao Carlos - SP, 13.560-970 - Brasil

Email:
Marinho@icmsc.usp.br

**J. B. R. do Val**

Affiliation:
Depto. de Telemática, Fac. de Eng. Elétrica, Universidade Estadual de Campinas - UNICAMP, C.P. 6101, 13081-970 - Campinas - SP, Brasil

Email:
jbosco@dt.fee.unicamp.br

DOI:
https://doi.org/10.1090/S0025-5718-97-00825-9

Keywords:
Numerical solutions for partial differential equations,
elliptic differential equations,
Helmholtz equations,
non-standard difference approximation,
convection-diffusion equations

Received by editor(s):
July 31, 1995

Additional Notes:
This work was partially supported by CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico, grant number 300573/95-2(NV) and 300721/86-2(NV)

Article copyright:
© Copyright 1997
American Mathematical Society