Iterative refinement of finite element approximations for elliptic problems. (English) Zbl 0481.65064


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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[1] F. CHATELIN, Linear spectral approximation in Banach spaces (to appear). · Zbl 0517.65036
[2] P. G. CIARLET, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). Zbl0383.65058 MR520174 · Zbl 0383.65058
[3] D. GILBARG and N. S. TRUDINGER, Elliptic partial differential equations of second order.Springer-Verlag, Berlin-Heidelberg-New York (1977). Zbl0361.35003 MR473443 · Zbl 0361.35003
[4] W. HACKBUSCH, Bemerkungen zur iterierten Defektkorrektur. (To appear in Rev.Roumaine Math. Pure Appl.) (1981). MR646400 · Zbl 0475.65030
[5] Lin QUN, Some problems about the approximate solution for operator equations. Acta Math. Sinica 22 (1979) 219-230. Zbl0397.65070 MR542459 · Zbl 0397.65070
[6] Lin QUN, Method to increase the accuracy of Lowe-degree finite element solutions... Computing Methods in Applied Sciences and Engineering, North-Holland, Amsterdam (1980). Zbl0438.73056 MR584026 · Zbl 0438.73056
[7] J. NITSCHE, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer.Math. 11 (1968) 346-348. Zbl0175.45801 MR233502 · Zbl 0175.45801 · doi:10.1007/BF02166687
[8] A. H. SCHATZ, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms. Math. Comp. 28 (1974) 959-962. Zbl0321.65059 MR373326 · Zbl 0321.65059 · doi:10.2307/2005357
[9] I. H. SLOAN, Improvement by iteration for compact operator equations. Math. Comp. 30(1976) 758-764. Zbl0343.45010 MR474802 · Zbl 0343.45010 · doi:10.2307/2005396
[10] H. STETTER, The defect correction principle and discretization methods. Numer. Math.29 (1978) 425-443. Zbl0362.65052 MR474803 · Zbl 0362.65052 · doi:10.1007/BF01432879
[11] G. STRANG and G FIX, Analysis of the finite element method. Prentice-Hall, EnglewoodCliffs,N. J. (1973). Zbl0356.65096 MR443377 · Zbl 0356.65096
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