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Nedoma, Josef

The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements. (English) Zbl 0413.65080

RAIRO, Anal. Numér. 13, 257-289 (1979).
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Cited in 1 Review
Cited in 5 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations

Keywords:

error bounds; approximate solutions; parabolic equations; finite element method; \(A\)-stable methods; elliptic equations
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\textit{J. Nedoma}, RAIRO, Anal. Numér. 13, 257--289 (1979; Zbl 0413.65080)
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References:

[1] 1. J. H. BRAMBLE and S. R. HILBERT, Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation, S.I.A.M. J. Numer. Anal., Vol. 7, 1970, pp. 112-124. Zbl0201.07803 MR263214 · Zbl 0201.07803 · doi:10.1137/0707006
[2] 2. J. H. BRAMBLE and M. ZLÁMAL, Triangular Elements in the Finite Element Method, Math. Comp., Vol. 24, 1970, pp. 809-820. Zbl0226.65073 MR282540 · Zbl 0226.65073 · doi:10.2307/2004615
[3] 3. P. G. CIARLET and P. A. RAVIART, The Combined Effect of Curved Boundaries and Numerical Integration in Isoparametric Finite Element Methods, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. K. Aziz, Ed., Academic Press, New York, 1972, pp. 409-474. Zbl0262.65070 MR421108 · Zbl 0262.65070
[4] 4. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1977. Zbl0383.65058 MR520174 · Zbl 0383.65058
[5] 5. P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York-London, 1962. Zbl0112.34901 MR135729 · Zbl 0112.34901
[6] 6. J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. Zbl1225.35003 MR227584 · Zbl 1225.35003
[7] 7. J. NEDOMA, The Finite Element solution of Parabolic Equations, Aplikace matematiky, svazek, 23, 1978, Č 6, pp. 408-438. Zbl0427.65075 MR508545 · Zbl 0427.65075
[8] 8. P. A. RAVIART, The Use of Numerical Integration in Finite Element Methods for Solving Parabolic Equations, Conference on Numerical Analysis, Dublin, August 14-18, 1972. Zbl0293.65086 MR345428 · Zbl 0293.65086
[9] 9. G. STRANG, Approximation in the Finite Element Method, Numer. Math., Vol. 19, 1972, pp. 81-98. Zbl0221.65174 MR305547 · Zbl 0221.65174 · doi:10.1007/BF01395933
[10] 10. M. ZLÁMAL, Finite Element Multistep Discretizations of Parabolic Boundary Value Problems, Mathematics of Computation, Vol. 29, No. 130, April 1975, pp. 350-359. Zbl0302.65081 MR371105 · Zbl 0302.65081 · doi:10.2307/2005556
[11] 11. M. ZLÁMAL, Curved Elements in the Finite Element Method I. S.I.A.M. J. Numer. Anal., Vol. 10, No. 1, March 1973. Zbl0285.65067 MR395263 · Zbl 0285.65067 · doi:10.1137/0710022
[12] 12. M. ZLÁMAL, Curved Elements in the Finite Element Method II. S.I.A.M. J. Numer. Anal., Vol. 11, No. 2, April 1974. Zbl0277.65064 MR343660 · Zbl 0277.65064 · doi:10.1137/0711031
[13] 13. M. ZLÁMAL, Finite Element Methods for Parabolic Equations. Mathematics of Computation, Vol. 28, No. 126, April 1974, pp. 393-409. Zbl0296.65054 MR388813 · Zbl 0296.65054 · doi:10.2307/2005915
[14] 14. M. ZLÁMAL, Finite Element Methods for Nonlinear Parabolic Equations, R.A.I.R.O., Vol. 11, No. 1, 1971, pp. 93-107. Zbl0385.65049 MR502073 · Zbl 0385.65049
[15] 15. A. ŽENIŠEK, Curved Triangular Finite C m -Elements, Aplikace matematiky, svazek 23, 1978, Č. 5, pp. 346-377. Zbl0404.35041 MR502072 · Zbl 0404.35041
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