A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampere equation

This paper develops a new recovery-based linear C-0 finite element method for approximating the weak solution of a fourth-order singularly perturbed Monge-Ampere equation, which is known as the vanishing moment approximation of the Monge-Ampere equation. The proposed method uses a gradient recovery technique to define a discrete Laplacian for a given linear C-0 finite element function (offline), the discrete Laplacian is then employed to discretize the biharmonic operator appeared in the equation. It is proved that the proposed C-0 linear finite element method has a unique solution using a fixed point argument and the corresponding error estimates are derived in various norms. Numerical experiments are also provided to verify the theoretical error estimates and to demonstrate the efficiency of the proposed recovery-based linear C-0 finite element method.