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Volume 11, Issue 3
Numerical Approximation to a Stochastic Parabolic PDE with Weak Galerkin Method

Hongze Zhu, Yongkui Zou, Shimin Chai & Chenguang Zhou

DOI: 10.4208/nmtma.2017-OA-0122

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 604-617.

Published online: 2018-11

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  • Abstract

The weak Galerkin finite element method is a class of recently and rapidly developed numerical tools for approximating partial differential equations. Unlike the standard Galerkin method, its trial and test function spaces consist of totally discontinuous piecewisely defined polynomials in the whole domain. This method has been vastly applied to many fields [22, 28, 31, 44, 50-52]. In this paper, we will apply this method to approximate a stochastic parabolic partial differential equation. We set up a semi-discrete numerical scheme for the stochastic partial differential equations and derive the optimal order for error estimates in the sense of strong convergence.

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@Article{NMTMA-11-604, author = {Hongze Zhu, Yongkui Zou, Shimin Chai and Chenguang Zhou}, title = {Numerical Approximation to a Stochastic Parabolic PDE with Weak Galerkin Method}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {3}, pages = {604--617}, abstract = {

The weak Galerkin finite element method is a class of recently and rapidly developed numerical tools for approximating partial differential equations. Unlike the standard Galerkin method, its trial and test function spaces consist of totally discontinuous piecewisely defined polynomials in the whole domain. This method has been vastly applied to many fields [22, 28, 31, 44, 50-52]. In this paper, we will apply this method to approximate a stochastic parabolic partial differential equation. We set up a semi-discrete numerical scheme for the stochastic partial differential equations and derive the optimal order for error estimates in the sense of strong convergence.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017-OA-0122}, url = {http://global-sci.org/intro/article_detail/nmtma/12446.html} }
TY - JOUR T1 - Numerical Approximation to a Stochastic Parabolic PDE with Weak Galerkin Method AU - Hongze Zhu, Yongkui Zou, Shimin Chai & Chenguang Zhou JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 604 EP - 617 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.2017-OA-0122 UR - https://global-sci.org/intro/article_detail/nmtma/12446.html KW - AB -

The weak Galerkin finite element method is a class of recently and rapidly developed numerical tools for approximating partial differential equations. Unlike the standard Galerkin method, its trial and test function spaces consist of totally discontinuous piecewisely defined polynomials in the whole domain. This method has been vastly applied to many fields [22, 28, 31, 44, 50-52]. In this paper, we will apply this method to approximate a stochastic parabolic partial differential equation. We set up a semi-discrete numerical scheme for the stochastic partial differential equations and derive the optimal order for error estimates in the sense of strong convergence.

Hongze Zhu, Yongkui Zou, Shimin Chai and Chenguang Zhou. (2018). Numerical Approximation to a Stochastic Parabolic PDE with Weak Galerkin Method. Numerical Mathematics: Theory, Methods and Applications. 11 (3). 604-617. doi:10.4208/nmtma.2017-OA-0122
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