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A numerical scheme based on mean value solutions for the helmholtz equation on triangular grids
Author(s):
M.
G.
Andrade;
J.
B. R.
do Val.
Journal:
Math. Comp.
66
(1997),
477-493.
MSC (1991):
Primary 35A40, 65N06;
Secondary 35J25, 65N15, 65N22
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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:
10.1090/S0025-5718-97-00825-9
PII:
S 0025-5718(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)
Copyright of article:
Copyright
1997,
American Mathematical Society
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