Abstract
We consider an explicit estimation for error constants from two basic constant interpolations on triangular finite elements. The problem of estimating the interpolation constants is related to the eigenvalue problems of the Laplacian with certain boundary conditions. By adopting the Lehmann-Goerisch theorem and finite element spaces with a variable mesh size and polynomial degree, we succeed in bounding the leading eigenvalues of the Laplacian and the error constants with high precision. An online demo for the constant estimation is also available at http://www.xfliu.org/onlinelab/.
Original language | English |
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Pages (from-to) | 635-652 |
Number of pages | 18 |
Journal | Japan Journal of Industrial and Applied Mathematics |
Volume | 30 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2013 Nov |
Keywords
- Eigenvalue problem
- Finite element method
- Interpolation error constants
- Lehmann-Goerisch theorem
- hp-FEM
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics