A C-weak Galerkin Finite Element Method for the Biharmonic Equation
نویسندگان
چکیده
Abstract. A C0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C0 functions in the new weak formulation. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established in both a discrete H2 norm and the L2 norm, for the weak Galerkin finite element solution. Numerical results are presented to confirm the theory. As a technical tool, a refined Scott-Zhang interpolation operator is constructed to assist the corresponding error estimate. This refined interpolation preserves the volume mass of order (k + 1 − d) and the surface mass of order (k + 2− d) for the Pk+2 finite element functions in d-dimensional space.
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