Durán, Ricardo G.; Gastaldi, Lucia; Padra, Claudio A posteriori error estimators for mixed approximations of eigenvalue problems. (English) Zbl 1012.65112 Math. Models Methods Appl. Sci. 9, No. 8, 1165-1178 (1999). Summary: We introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart-Thomas of the lowest order. We define an error estimator of the residual type which can be computed locally from the approximate eigenvector and prove that the estimator is equivalent to the norm of the error in the approximation of the eigenvector up to higher-order terms. The constants involved in this equivalence depend on the corresponding eigenvalue but are independent of the mesh size, provided the meshes satisfy the usual minimum angle condition. Moreover, the square root of the error in the approximation of the eigenvalue is also bounded by a constant times the estimator. Cited in 39 Documents MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:error bounds; eigenvalues; eigenvectors; second-order elliptic problem; mixed finite element method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1007/s002110050222 · Zbl 0866.65068 · doi:10.1007/s002110050222 [2] Arnold D. N., Modél. Math. Anal. Numer. 19 pp 7– (1985) · Zbl 0567.65078 · doi:10.1051/m2an/1985190100071 [3] DOI: 10.1002/nme.1620121010 · Zbl 0396.65068 · doi:10.1002/nme.1620121010 [4] DOI: 10.1002/(SICI)1097-0207(19970430)40:8<1435::AID-NME119>3.0.CO;2-P · doi:10.1002/(SICI)1097-0207(19970430)40:8<1435::AID-NME119>3.0.CO;2-P [5] DOI: 10.1016/0045-7825(94)90095-7 · Zbl 0851.73053 · doi:10.1016/0045-7825(94)90095-7 [6] DOI: 10.1090/S0025-5718-97-00837-5 · Zbl 0864.65068 · doi:10.1090/S0025-5718-97-00837-5 [7] DOI: 10.1002/nme.1620290402 · Zbl 0724.73173 · doi:10.1002/nme.1620290402 [8] Clement P., Anal. Numer. 9 pp 77– (1975) [9] DOI: 10.1090/S0025-5718-1995-1284666-9 · doi:10.1090/S0025-5718-1995-1284666-9 [10] Dari E., Math. Model. Numer. Anal. 30 pp 385– (1996) · Zbl 0853.65110 · doi:10.1051/m2an/1996300403851 [11] DOI: 10.1007/s002110050212 · Zbl 0857.76041 · doi:10.1007/s002110050212 [12] DOI: 10.1002/nme.1620130110 · Zbl 0384.76060 · doi:10.1002/nme.1620130110 [13] DOI: 10.1137/0722029 · Zbl 0573.65082 · doi:10.1137/0722029 [14] DOI: 10.1090/S0025-5718-1981-0606505-9 · doi:10.1090/S0025-5718-1981-0606505-9 [15] DOI: 10.1090/S0025-5718-96-00739-9 · Zbl 0853.65111 · doi:10.1090/S0025-5718-96-00739-9 [16] DOI: 10.1090/S0025-5718-1990-1011446-7 · doi:10.1090/S0025-5718-1990-1011446-7 [17] DOI: 10.1007/BF01390056 · Zbl 0674.65092 · doi:10.1007/BF01390056 [18] DOI: 10.2307/2153518 · Zbl 0799.65112 · doi:10.2307/2153518 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.