A computational study of the weak Galerkin method for second-order elliptic equations
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The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye (2011) for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established in Wang and Ye (2011). The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.
KeywordsFinite element methods Weak Galerkin methods Elliptic equations
Mathematics Subject Classifications (2010)Primary 65N30; Secondary 65N50
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- 5.Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer (1991)Google Scholar
- 10.Lin, M., Wang, J., Ye, X.: Weak Galerkin finite element methods for second-order elliptic problems on polytopal meshes. arXiv:1204.3655v1 [math.NA]
- 12.Raviart, P., Thomas, J.: A mixed finite element method for second order elliptic problems. In: Galligani, I., Magenes, E. (eds.) Mathematical Aspects of the Finite Element Method, Lectures Notes in Math. 606. Springer, New York (1977)Google Scholar
- 13.Wang, J., Ye, X.: A weak Galerkin finite element method for second-order elliptic problems. arXiv:1104.2897v1 [math.NA] (2011)
- 14.Wang, J., Ye, X.: A weak Galerkin mixed finite element method for second-order elliptic problems. arXiv:1104.2897v1 [math.NA]