A C0‐weak Galerkin finite element method for fourth‐order elliptic problems

This article proposes and analyzes a C⁰‐weak Galerkin (WG) finite element method for solving the biharmonic equation in two‐dimensional and three‐dimensional. The new WG method uses continuous piecewise‐polynomial approximations of degree for the unknown u and discontinuous piecewise‐polynomial approximations of degree k for the trace of on the interelement boundaries. Optimal error estimates are obtained in H², H¹, and L² norms. Numerical experiments illustrate and confirm the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1090–1104, 2016