A conforming DG finite element method is developed for the biharmonic equation on polytopal meshes, with optimal error estimates established in a discrete H2 norm and L2 estimates ranging from sub-optimal to optimal by element order.
On stabilizer-free weak Galerkin finite element methods on polytopal meshes
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abstract
A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods will simplify the formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin finite element method for second order elliptic equations on polytopal meshes in 2D or 3D. This new WG method keeps a simple symmetric positive definite form and can work on polygonal/polyheral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete $H^1$ norm and the $L^2$ norm. Numerical results are presented verifying the theorem.
fields
math.NA 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
A new stabilizer-free weak Galerkin method for the biharmonic equation achieves optimal error estimates in discrete H² (k≥2) and L² (k>2) on polytopal meshes.
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A conforming DG method for the biharmonic equation on polytopal meshes
A conforming DG finite element method is developed for the biharmonic equation on polytopal meshes, with optimal error estimates established in a discrete H2 norm and L2 estimates ranging from sub-optimal to optimal by element order.
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A stabilizer free weak Galerkin method for the Biharmonic Equation on Polytopal Meshes
A new stabilizer-free weak Galerkin method for the biharmonic equation achieves optimal error estimates in discrete H² (k≥2) and L² (k>2) on polytopal meshes.