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On the use of singular functions with finite element approximations. (English) Zbl 0273.35004

35A35Theoretical approximation to solutions of PDE
41A15Spline approximation
35J25Second order elliptic equations, boundary value problems
65N06Finite difference methods (BVP of PDE)
Full Text: DOI
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[2] Birkhoff, G.: Piecewise bicubic interpolation and approximation in polygons. Approximation with special emphasis on spline functions 1 (1969) · Zbl 0279.41003
[3] G. Birkhoff, Angular singularities of elliptic problems, J. Approximation Theory, to appear. · Zbl 0252.35003
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[10] Fix, G.: Higher-order Rayleigh-Ritz approximations. J. math. Mech. 18, 645-658 (1969) · Zbl 0234.65095
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[13] . ASTM special tech. Publ. no. 381 (1964)
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[18] Varga, R. S.: Functional analysis, approximation theory, and numerical analysis. SIAM rev. (1971) · Zbl 0226.65064
[19] Wait, R.; Mitchell, A. R.: Corner singularities in elliptic problems by finite element methods. J. computational phys. 8, 45-52 (1971) · Zbl 0224.65030
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[28] Kondrat’ev, V. A.: Boundary problems for elliptic equations with conical or angular points. Trans. Moscow math. Soc. 17 (1968)