Error estimates of H 1-Galerkin mixed finite element method for Schrödinger equation

Abstract

An H 1 -Galerkin mixed finite element method is discussed for a class of second order Schrodinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H 1 -Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.