Explicit Finite Element Error Estimates for Nonhomogeneous Neumann Problems
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.
Keywordsfinite element methods nonhomogeneous Neumann problems explicit error estimates
MSC 201065N15 65N30
Unable to display preview. Download preview PDF.
- I. Babuška, J. Osborn: Eigenvalue problems. Handbook of Numerical Analysis, Volume II: Finite Element Methods (Part 1) (P. G. Ciarlet, J. L. Lions, eds. ). North-Holland, Amsterdam, 1991, pp. 641–787.Google Scholar
- J. H. Bramble, J. E. Osborn: Approximation of Steklov eigenvalues of non-selfadjoint second order elliptic operators. Mathematical Foundations of the Finite Element Method with Applications to PDE (A. K. Aziz, ed. ). Academic Press, New York, 1972, pp. 387–408.Google Scholar
- K. Kobayashi: On the interpolation constants over triangular elements. Proceedings of the International Conference Applications of Mathematics 2015 (J. Brandts et al., eds. ). Czech Academy of Sciences, Institute of Mathematics, Praha, 2015, pp. 110–124.Google Scholar