A Variational Multiscale Method for Poisson’s Equation in Mixed Form

In this paper we present the adaptive variational multiscale method for solving the Poisson equation in mixed form. We use the method introduced in [3], and further analyzed and applied to mixed problems in [4], which is a general tool for solving linear partial differential equations with multiscale features in the coefficients. We extend the numerics in [4] from rectangular meshes to triangular meshes which allow for computation on more compli-cated domains. A new a posteriori error estimate is also included, which is used in an adaptive algorithm. We present a numerical example that shows the efficiency of incorporating a posteriori based adaptivity into the method.