Suboptimal and Optimal Convergence in Mixed Finite Element Methods

An elliptic partial differential equation may be formulated in different but equivalent ways, and the mixed finite element methods derived from these formulations have different properties. We give general error estimates for two such methods, which are always optimal for the Raviart– Thomas elements, but which are suboptimal for the Brezzi–Douglas–Marini elements in one of the methods. Computational experiments show that this suboptimal estimate is sharp.