A \(C^{0}\)-weak Galerkin finite element method for fourth-order elliptic problems (Q2808877)

This paper applies the \(C^0\)-weak Galerking finite element method to the biharmonic equation \(\Delta^2u = f\) in a polyhedral domain \(\Omega \subset \mathbb R^d\), \(d=2,3\), with boundary conditions \(u=g_1\) and \(\partial u/ \partial n = g_2\) on \(\partial\Omega\) and proves the corresponding a priori error estimates. A priori error estimates in \(L^2\) norms are obtained by the Aubin-Nitche duality argument. The paper is concluded by numerical experiments confirming the theoretical results.