The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements

Josef Nedoma

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1979)

  • Volume: 13, Issue: 3, page 257-289
  • ISSN: 0764-583X

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Nedoma, Josef. "The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 13.3 (1979): 257-289. <http://eudml.org/doc/193343>.

@article{Nedoma1979,
author = {Nedoma, Josef},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error bounds; approximate solutions; parabolic equations; finite element method; -stable methods; elliptic equations},
language = {eng},
number = {3},
pages = {257-289},
publisher = {Dunod},
title = {The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements},
url = {http://eudml.org/doc/193343},
volume = {13},
year = {1979},
}

TY - JOUR
AU - Nedoma, Josef
TI - The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1979
PB - Dunod
VL - 13
IS - 3
SP - 257
EP - 289
LA - eng
KW - error bounds; approximate solutions; parabolic equations; finite element method; -stable methods; elliptic equations
UR - http://eudml.org/doc/193343
ER -

References

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  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. Zbl0201.07803MR263214
  2. 2. J. H. BRAMBLE and M. ZLÁMAL, Triangular Elements in the Finite Element Method, Math. Comp., Vol. 24, 1970, pp. 809-820. Zbl0226.65073MR282540
  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. Zbl0262.65070MR421108
  4. 4. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1977. Zbl0383.65058MR520174
  5. 5. P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York-London, 1962. Zbl0112.34901MR135729
  6. 6. J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
  7. 7. J. NEDOMA, The Finite Element solution of Parabolic Equations, Aplikace matematiky, svazek, 23, 1978, Č 6, pp. 408-438. Zbl0427.65075MR508545
  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. Zbl0293.65086MR345428
  9. 9. G. STRANG, Approximation in the Finite Element Method, Numer. Math., Vol. 19, 1972, pp. 81-98. Zbl0221.65174MR305547
  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. Zbl0302.65081MR371105
  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. Zbl0285.65067MR395263
  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. Zbl0277.65064MR343660
  13. 13. M. ZLÁMAL, Finite Element Methods for Parabolic Equations. Mathematics of Computation, Vol. 28, No. 126, April 1974, pp. 393-409. Zbl0296.65054MR388813
  14. 14. M. ZLÁMAL, Finite Element Methods for Nonlinear Parabolic Equations, R.A.I.R.O., Vol. 11, No. 1, 1971, pp. 93-107. Zbl0385.65049MR502073
  15. 15. A. ŽENIŠEK, Curved Triangular Finite C m -Elements, Aplikace matematiky, svazek 23, 1978, Č. 5, pp. 346-377. Zbl0404.35041MR502072

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