Volume 12, Issue 1
Weak Galerkin Finite Element Methods on Polytopal Meshes

Lin Mu, Junping Wang & Xiu Ye

Int. J. Numer. Anal. Mod., 12 (2015), pp. 31-53.

Published online: 2015-12

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  • Abstract

This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed and why they provide reliable numerical approximations for the underlying partial differential equations. In particular, optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the WG-FEM. All the results are established for finite element partitions with polytopes that are shape regular.

  • Keywords

weak Galerkin, finite element methods, discrete gradient, second-order elliptic problems, polytopal meshes.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-31, author = {}, title = {Weak Galerkin Finite Element Methods on Polytopal Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {1}, pages = {31--53}, abstract = {

This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed and why they provide reliable numerical approximations for the underlying partial differential equations. In particular, optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the WG-FEM. All the results are established for finite element partitions with polytopes that are shape regular.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/477.html} }
TY - JOUR T1 - Weak Galerkin Finite Element Methods on Polytopal Meshes JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 31 EP - 53 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/477.html KW - weak Galerkin, finite element methods, discrete gradient, second-order elliptic problems, polytopal meshes. AB -

This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed and why they provide reliable numerical approximations for the underlying partial differential equations. In particular, optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the WG-FEM. All the results are established for finite element partitions with polytopes that are shape regular.

Lin Mu, Junping Wang & Xiu Ye. (1970). Weak Galerkin Finite Element Methods on Polytopal Meshes. International Journal of Numerical Analysis and Modeling. 12 (1). 31-53. doi:
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