On the Krylov maximum principle for discrete parabolic schemes

Abstract

In previous works, we have established discrete versions of the Krylov maximum principle for parabolic operators, on general meshes in Euclidean space. In this article, we prove a variant of these estimates in terms of a discrete analogue of the determinant of the coefficient matrix in the differential operator case. Our treatment adapts key ideas from our previous work on the corresponding discrete Aleksandrov maximum principle in the elliptic case.