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The finite element method for ill-posed problems. (English) Zbl 0369.65012

MSC:
65J05 General theory of numerical analysis in abstract spaces
65R20 Numerical methods for integral equations
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References:
[1] 1. A. K. AZIZ and I. BABUSKA, Survey Lectures on the Mathematical Foundations of the Finite Element Method. In : Aziz, A. K. (ed.) : The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations, Academic Press, 1972. Zbl0268.65052 MR421106 · Zbl 0268.65052
[2] 2. I. CEA, Optimisation, Théorie et Algorithmes. Dunod, Paris, 1971. Zbl0211.17402 MR298892 · Zbl 0211.17402
[3] 3. J. N. FRANKLIN. On Tikhonov’s Method for Ill-Posed Problems. Math. Comp. 28. 1974, p. 889-907 Zbl0297.65053 MR375817 · Zbl 0297.65053 · doi:10.2307/2005354
[4] 4. B. GUENTHER, E. K. KILLIAN, K. T. SMITH and S. L. WAGNER, Reconstruction of objects form Radiographs and the Location of Brain Tumors. Proc. at. Acad. Sci. USA. 71, 1974 p. 4884-4886. MR354065
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[7] 7. R. MITTRA and C. A. KLEIN, Stability and Convergence of Moment Method Solutions. In : MITTRA, R. (ed) : Numerical and Asymptotic Techniques in Electromagnetics, Spinger, 1975.
[8] 8. D. L. PHILIPPS. A Technique for the Numerical Solution of Certain Integral Equations ofthe First Kind. J. Ass. Comp. Mach. 9, 1962, p. 84-97. Zbl0108.29902 MR134481 · Zbl 0108.29902 · doi:10.1145/321105.321114
[9] 9. G. RIBIÈRE, Régularisation d’opérateurs. R.I.R.O., 1, 1967, p. 57-79. Zbl0184.37003 MR224267 · Zbl 0184.37003
[10] 10. A. N. TIKHONOV, The Regularization of Incorrectly Posed Problems. Dokl. Akad. Nauk SSSR, 153, 1963, p. 42-52. Zbl0183.11601 · Zbl 0183.11601
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