A domain decomposition and mixed method for a linear parabolic boundary value problem

In this paper, we discuss the convergence of a domain decomposition method for the solution of linear parabolic equations in their mixed formulations. The subdomain meshes need not be quasi-uniform; they are composed of triangles or quadrilaterals that do not match at interfaces. For the ease of computation, this lack of continuity is compensated by a mortar technique based on piecewise constant (discontinuous) multipliers. It is shown that the method on triangles, parallelograms or slightly distorted parallelograms is convergent at the expense of a half-order loss of accuracy compared with mortar methods based on piecewise linear multipliers.