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In this paper we propose a way of enhancing eigenvalue approximations with the Bank--Weiser error estimators for the $P1$ and $P2$ conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.
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참고문헌 (22)
참고문헌 신청
P. Amore / 2016 / High or-der eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences / J. Comput. Phys 312:252~271
I. Babuˇska / 1989 / Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems / Math. Comp 52:275~297
I. Babuska / 1991 / Handbook of Numeri-cal Analysis II, Finite Element Methods (Part 1) :641~787
R. E. Bank / 1985 / Some a posteriori error estimators for elliptic partial differential equations / Math. Comp 44:283~301
R. E. Bank / 2003 / Asymptotically exact a posteriori error estimators, Part I: Grids with superconvergence / SIAM J. Numer. Anal 41:2294~2312
I. Babuˇska / 1989 / Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems / Math. Comp 52:275~297
I. Babuska / 1991 / Handbook of Numeri-cal Analysis II, Finite Element Methods (Part 1) :641~787
R. E. Bank / 1985 / Some a posteriori error estimators for elliptic partial differential equations / Math. Comp 44:283~301
R. E. Bank / 2003 / Asymptotically exact a posteriori error estimators, Part I: Grids with superconvergence / SIAM J. Numer. Anal 41:2294~2312
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