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Volume 12, Issue 2
A Hybridized Weak Galerkin Finite Element Method for the Biharmonic Equation

Chunmei Wang & Junping Wang

Int. J. Numer. Anal. Mod., 12 (2015), pp. 302-317.

Published online: 2015-12

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  • Abstract

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An error estimate of optimal order is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknowns associated with the interior variables on each element, yielding a significantly reduced system of linear equations for unknowns on the element interfaces.

  • Keywords

Weak Galerkin, hybridized weak Galerkin, finite element methods, weak Hessian, biharmonic problems.

  • AMS Subject Headings

365N30, 65N15, 65N12, 74N20, Secondary, 35B45, 35J50, 35J35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-302, author = {Chunmei Wang and Junping Wang}, title = {A Hybridized Weak Galerkin Finite Element Method for the Biharmonic Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {302--317}, abstract = {

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An error estimate of optimal order is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknowns associated with the interior variables on each element, yielding a significantly reduced system of linear equations for unknowns on the element interfaces.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/490.html} }
TY - JOUR T1 - A Hybridized Weak Galerkin Finite Element Method for the Biharmonic Equation AU - Chunmei Wang & Junping Wang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 302 EP - 317 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/490.html KW - Weak Galerkin, hybridized weak Galerkin, finite element methods, weak Hessian, biharmonic problems. AB -

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An error estimate of optimal order is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknowns associated with the interior variables on each element, yielding a significantly reduced system of linear equations for unknowns on the element interfaces.

Chunmei Wang and Junping Wang. (2015). A Hybridized Weak Galerkin Finite Element Method for the Biharmonic Equation. International Journal of Numerical Analysis and Modeling. 12 (2). 302-317. doi:
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