Finite element methods of optimal order for problems with singular data
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- by Kenneth Eriksson PDF
- Math. Comp. 44 (1985), 345-360 Request permission
Abstract:
An adapted finite element method is proposed for a class of elliptic problems with singular data. The idea is to subtract the main singularity from the solution and to solve for the remainder using suitable mesh-refinements. Optimal order error estimates are proved.References
- Ivo Babuška, Error-bounds for finite element method, Numer. Math. 16 (1970/71), 322–333. MR 288971, DOI 10.1007/BF02165003
- Ivo Babuška and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 1–359. With the collaboration of G. Fix and R. B. Kellogg. MR 0421106
- J. H. Bramble and A. H. Schatz, Estimates for spline projections, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. 10 (1976), no. R-2, 5–37. MR 0436620
- Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
- Philippe G. Ciarlet, Discrete variational Green’s function. I, Aequationes Math. 4 (1970), 74–82. MR 273838, DOI 10.1007/BF01817748 K. Eriksson, Improved Convergence by Mesh-Refinement in the Finite Element Method, Thesis, Chalmers University of Technology and the University of Göteborg, 1981.
- Kenneth Eriksson, Improved accuracy by adapted mesh-refinements in the finite element method, Math. Comp. 44 (1985), no. 170, 321–343. MR 777267, DOI 10.1090/S0025-5718-1985-0777267-3 Ju. P. Krasovskiǐ, "Isolation of singularities of the Green’s function," Math. USSR-Izv., v. 1, 1967, pp. 935-966.
- J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
- A. H. Schatz and L. B. Wahlbin, Interior maximum norm estimates for finite element methods, Math. Comp. 31 (1977), no. 138, 414–442. MR 431753, DOI 10.1090/S0025-5718-1977-0431753-X
- Ridgway Scott, Finite element convergence for singular data, Numer. Math. 21 (1973/74), 317–327. MR 337032, DOI 10.1007/BF01436386
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Math. Comp. 44 (1985), 345-360
- MSC: Primary 65N30; Secondary 65N50
- DOI: https://doi.org/10.1090/S0025-5718-1985-0777268-5
- MathSciNet review: 777268