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Type: Artigo de periódico
Title: A numerical scheme based on mean value solutions for the Helmholtz equation on triangular grids
Author: Andrade, MG
DoVal, JBR
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 O(h(4)) accuracy. Some numerical examples are discussed and the results are compared with other methods, with a consistent advantage to the solution obtained here.
Subject: numerical solutions for partial differential equations
elliptic differential equations
Helmholtz equations
non-standard difference approximation
convection-diffusion equations
Editor: Amer Mathematical Soc
Rights: aberto
Identifier DOI: 10.1090/S0025-5718-97-00825-9
Date Issue: 1997
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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