On the Stability and Convergence of Higher-order Mixed Finite Element Methods for Second-order Elliptic Problems

We investigate the use of higher-order mixed methods for secondorder elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size h and polynomial degree p . Our estimates yield asymptotic convergence rates for the pand h p-versions of the finite element method. They also describe more accurately than previously proved estimates the increased rate of convergence expected when the /¡-version is used with higher-order polynomials. For our analysis, we choose the Raviart-Thomas and the Brezzi-Douglas-Marini elements and establish optimal rates of convergence in both h and p (up to arbitrary e > 0 ).