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Mixed-hybrid finite element approximations of second-order elliptic boundary value problems. Part 2: Weak-hybrid methods. (English) Zbl 0401.65068


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0382.65056
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Full Text: DOI

References:

[1] I. Babuska, J.T. Oden and J.K. Lee, Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, Comp. Meth. Appl. Mech. Eng. 00 (0000) 000-000.; I. Babuska, J.T. Oden and J.K. Lee, Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, Comp. Meth. Appl. Mech. Eng. 00 (0000) 000-000.
[2] Rose, E. M., Finite difference schemes for differential equations, Math. Comp., 18, 179-195 (1964) · Zbl 0122.12301
[3] Schultz, M. H.; Varga, R. S., \(L\)-splines, Numer. Math., 10, 345-369 (1967) · Zbl 0183.44402
[4] Greenstaat, J., Cell discretization, (Conference on Application of Numerical Analysis. Conference on Application of Numerical Analysis, Springer Lecture Notes in Math. (1971)), 70-86, No. 228
[5] Hoppe, V., Finite elements with harmonic interpolation functions, (Whiteman, J. R., The mathematics of finite elements and applications (1973), Academic Press: Academic Press London), 131-142
[6] Rose, M. E., Weak-element approximation and applications to the scattering of plane waves by a potential (1971), Preprint
[7] Rose, M. E., Weak-element approximation to elliptic differential equations, Numer. Math., 24, 185-209 (1975) · Zbl 0294.35028
[8] Babuska, I., Method of weak elements, (Tech. Note BN-809, BN-809 (Dec. 1974), Univ. of Maryland, Institute for Fluid Dynamics and Applied Mathematics) · Zbl 0665.73060
[9] Curtiss, J. H., Interpolation by harmonic polynomials, J. SIAM, 10, 709-736 (1962) · Zbl 0108.05701
[10] Curtiss, J. H., Solution of the Dirichlet problem by interpolating harmonic polynomials, Bull. Amer. Math. Soc., 68, 333-337 (1962) · Zbl 0107.06001
[11] Babuska, I.; Aziz, A. K., Survey lectures on the mathematical theory of finite elements, (Aziz, A. K., The mathematical foundations of the finite element method with applications to partial differential equations (1972), Academic Press: Academic Press New York), 3-359
[12] Oden, J. T.; Reddy, J. N., An introduction to the mathematical theory of finite elements (1976), Wiley-Interscience: Wiley-Interscience New York · Zbl 0336.35001
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