TY - JOUR
T1 - A Conforming DG Method for the Biharmonic Equation on Polytopal Meshes
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 855
EP - 869
PY - 2023
DA - 2023/11
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1037
UR - https://global-sci.org/intro/article_detail/ijnam/22144.html
KW - finite element methods, weak Laplacian, biharmonic equations, polyhedral meshes.
AB - <p style="text-align: justify;">A conforming discontinuous Galerkin finite element method is introduced for solving
the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps
simple formulation of the conforming finite element method at the same time. The ultra simple
formulation of the method will reduce programming complexity in practice. Optimal order error
estimates in a discrete $H^2$ norm is established for the corresponding finite element solutions. Error
estimates in the $L^2$ norm are also derived with a sub-optimal order of convergence for the lowest
order element and an optimal order of convergence for all high order of elements. Numerical
results are presented to confirm the theory of convergence.</p>