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 second-order 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 p- and 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 h-version is used with higher-order polynomials