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In this paper we present a postprocessing scheme for the Raviart--Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.
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참고문헌 (17)
참고문헌 신청
A. Alonso. / 2000 / A posteriori error estimates in finite element acoustic analysis / J. Comput. Appl. Math. 117:105~119
I. Babuska / 1991 / Eigenvalue Problems, in Handbook of Numerical Analysis II, Finite Element Methods (Part 1) :641~787
D. Boffi / 2010 / Finite element approximation of eigenvalue problems / Acta Numer. 19:1~120
D. Boffi / 1997 / On the convergence of eigenvalues for mixed formulations / Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25:131~154
D. Boffi / 2000 / On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form / Math. Comp. 69:121~140
I. Babuska / 1991 / Eigenvalue Problems, in Handbook of Numerical Analysis II, Finite Element Methods (Part 1) :641~787
D. Boffi / 2010 / Finite element approximation of eigenvalue problems / Acta Numer. 19:1~120
D. Boffi / 1997 / On the convergence of eigenvalues for mixed formulations / Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25:131~154
D. Boffi / 2000 / On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form / Math. Comp. 69:121~140
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