Guaranteed high-precision estimation for P-0 interpolation constants on triangular finite elements

作者：Liu Xuefeng^*; Oishi Shin'ichi

来源：Japan Journal of Industrial and Applied Mathematics, 2013, 30(3): 635-652.

DOI：10.1007/s13160-013-0120-6

• Interpolation error constants
• Eigenvalue problem
• Finite element method
• Lehmann-Goerisch theorem
• hp-FEM

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/.

• 出版日期2013