Error estimates of the discretization of linear parabolic equations on general nonconforming spatial grids
Abdallah Bradji, Jürgen Fuhrmann · Comptes Rendus Mathématique · 2010
A general class of nonconforming meshes has been recently used to approximate stationary anisotropic heterogeneous diffusion problems in any space dimensions. The aim of the present work is to deal with some error estimates of the discretization of parabolic equations on this general class of meshes in several space dimensions. We present an implicit scheme based on an orthogonal projection of the exact initial function. We provide error estimates in discrete norms L ∞ ( 0 , T ; H 0 1 ( Ω ) ) and W 1 , ∞ ( 0 , T ; L 2 ( Ω ) ) .