Explicit Finite Element Error Estimates for Nonhomogeneous Neumann problems
Provides explicit error bounds for finite element methods in a specific class of PDE problems, which is incremental for numerical analysis researchers.
The paper develops an explicit a priori error estimate for finite element solutions to nonhomogeneous Neumann problems, achieving a convergence rate of 0.5 as demonstrated by numerical examples.
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 $0.5$.