Explicit Finite Element Error Estimates for Nonhomogeneous Neumann problems

Abstract

The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle equation over finite element spaces is constructed and the explicit upper bound of the constant in the trace theorem is given. Numerical examples are shown in the final section, which implies the proposed error {estimate} has the convergence rate as $0.5$.