TY - JOUR
T1 - Convergent Finite Elements on Arbitrary Meshes, the WG Method
AU - Zhang , Ran
AU - Zhang , Shangyou
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 651
EP - 665
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0038
UR - https://global-sci.org/intro/article_detail/csiam-am/24499.html
KW - Discontinuous finite element, maximum angle condition, Poisson’s equation, triangular grid, tetrahedral grid.
AB - <p style="text-align: justify;">On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not converge
to the true solution when the mesh size goes to zero. It is shown that one type of weak
Galerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e. on arbitrary meshes. Numerical tests confirm
the theory.</p>