Galerkin-type methods for strictly parabolic equations on compact Riemannian manifolds

Abstract

. We prove existence of weak solutions to the Cauchy problem cor- responding to various strictly parabolic equations on a compact Riemannian manifold ( M,g ). This also includes strictly parabolic equations with stochas- tic forcing with linear diffusion. Existence is proved through a variant of the Galerkin method and can be used to construct a convergent finite element method.