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 - <p style="text-align: justify;">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.</p>