Explicit Consistency Error Estimate for Finite Element Solutions of the Poisson Equation on Convex Domains

Abstract

We derive explicit a priori consistency error estimates for a standard finite element discretization of the Poisson equation on convex domains, where the domain is approximated by an internal convex polyhedron. The obtained explicit estimates depend only on global geometric parameters and are applicable to general convex domains and arbitrary families of simplicial meshes.

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