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Volume 26, Issue 5
Finite Element and Discontinuous Galerkin Method for Stochastic Helmholtz Equation in Two- and Three-Dimensions

Yanzhao Cao, Ran Zhang & Kai Zhang

J. Comp. Math., 26 (2008), pp. 702-715.

Published online: 2008-10

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  • Abstract

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in $\mathbb{R}^d$ ($d$=2,3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.

  • Keywords

Stochastic partial differential equation, Finite element method, Discontinuous Galerkin method, Stochastic Helmholtz equation.

  • AMS Subject Headings

65N30, 65N15, 65C30, 60H15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-702, author = {Yanzhao Cao, Ran Zhang and Kai Zhang }, title = {Finite Element and Discontinuous Galerkin Method for Stochastic Helmholtz Equation in Two- and Three-Dimensions}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {702--715}, abstract = {

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in $\mathbb{R}^d$ ($d$=2,3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8653.html} }
TY - JOUR T1 - Finite Element and Discontinuous Galerkin Method for Stochastic Helmholtz Equation in Two- and Three-Dimensions AU - Yanzhao Cao, Ran Zhang & Kai Zhang JO - Journal of Computational Mathematics VL - 5 SP - 702 EP - 715 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8653.html KW - Stochastic partial differential equation, Finite element method, Discontinuous Galerkin method, Stochastic Helmholtz equation. AB -

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in $\mathbb{R}^d$ ($d$=2,3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.

Yanzhao Cao, Ran Zhang and Kai Zhang . (2008). Finite Element and Discontinuous Galerkin Method for Stochastic Helmholtz Equation in Two- and Three-Dimensions. Journal of Computational Mathematics. 26 (5). 702-715. doi:
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