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), 477493
MSC (1991):
Primary 35A40, 65N06; Secondary 35J25, 65N15, 65N22
MathSciNet review:
1401937
Fulltext PDF Free Access
Abstract 
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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 convectiondiffusion 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, 13.560970  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, 13081970  Campinas  SP, Brasil
Email:
jbosco@dt.fee.unicamp.br
DOI:
http://dx.doi.org/10.1090/S0025571897008259
PII:
S 00255718(97)008259
Keywords:
Numerical solutions for partial differential equations,
elliptic differential equations,
Helmholtz equations,
nonstandard difference approximation,
convectiondiffusion 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 300573/952(NV) and 300721/862(NV)
Article copyright:
© Copyright 1997
American Mathematical Society
