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On a dimensional reduction method. III: A posteriori error estimation and an adaptive approach. (English) Zbl 0523.65079


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74K15 Membranes
35J40 Boundary value problems for higher-order elliptic equations
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[1] Ivo Babuška and Werner C. Rheinboldt, Reliable error estimation and mesh adaptation for the finite element method, Computational methods in nonlinear mechanics (Proc. Second Internat. Conf., Univ. Texas, Austin, Tex., 1979) North-Holland, Amsterdam-New York, 1980, pp. 67 – 108.
[2] Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. · Zbl 0328.47035
[3] V. Dunder & S. Ridlon, ”Practical applications of the finite element method,” ASCE J. Structures Division ST1, January 1978, pp. 9-21.
[4] N. Dunford & J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
[5] M. Vogelius, Ph.D. Thesis, University of Maryland, December 1979.
[6] M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31 – 46. , https://doi.org/10.1090/S0025-5718-1981-0616358-0 M. Vogelius and I. Babuška, On a dimensional reduction method. II. Some approximation-theoretic results, Math. Comp. 37 (1981), no. 155, 47 – 68. , https://doi.org/10.1090/S0025-5718-1981-0616359-2 M. Vogelius and I. Babuška, On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach, Math. Comp. 37 (1981), no. 156, 361 – 384.
[7] M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31 – 46. , https://doi.org/10.1090/S0025-5718-1981-0616358-0 M. Vogelius and I. Babuška, On a dimensional reduction method. II. Some approximation-theoretic results, Math. Comp. 37 (1981), no. 155, 47 – 68. , https://doi.org/10.1090/S0025-5718-1981-0616359-2 M. Vogelius and I. Babuška, On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach, Math. Comp. 37 (1981), no. 156, 361 – 384.
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