A Hessian recovery-based finite difference method for biharmonic problems. (March 2023) - Xu, Minqiang; Shi, Chungang
Abstract: In this paper, we study a new finite difference method by combining Hessian recovery techniques and the ghost points method for biharmonic equations. Numerical results validate that our proposed method has optimal convergence orders in the L 2 norm and H 1 seminorm. Moreover, superconvergence properties of the recovered gradient and Hessian have been observed.