Explicit finite element error estimates for nonhomogeneous Neumann problems

[摘要] The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle 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 $0.5$.

[学科分类] 应用数学

[关键词] finite element methods;nonhomogeneous Neumann problems;explicit error estimates