Mixed finite element method for the heat diffusion equation in a random medium

Abstract

We introduce the dual mixed method for the heat evolution equation in a polygonal domain D with a random heat conduction coefficient and heat flux , ⋄ denoting the Wick product. We prove a priori error estimates for the semi-discrete solution of lowest order of the dual mixed method having K-dimensional polynomial chaos expansion of degree N. Due to the re-entrant corner of the polygonal domain D, appropriate refinement rules must be imposed on the family of triangulations in order to recapture convergence of order one in space.