A mixed finite element method for a sixth-order elliptic problem

Abstract

We consider a saddle-point formulation for a sixth-order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet–Raviart formulation for the biharmonic problem to formulate our saddle-point problem and the finite element method. The new formulation allows us to use the |$H^1$|-conforming Lagrange finite element spaces to approximate the solution. We prove a priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.