Mixed Discontinuous Galerkin Method for One-dimensional Biharmonic Equations without Penalty Terms

Abstract

In this paper, we apply a discontinuous Galerkin method without penalty terms for the solution of biharmonic equations in one-dimensional space. It overcomes the trouble of choosing appropriate penalty parameters to ensure the stability of discrete problems when solving biharmonic problems by discontinuous Galerkin methods. We first introduce an auxiliary variable p = uxx to transform the original problem into a second-order system. The variational formulation without interior penalty is derived, the well-posedness is present, and the optimal convergence rates under the energy norm and L 2 norm are obtained. Finally, several numerical findings demonstrate its accuracy and capability.