Reduced continuity finite element methods for first order scalar hyperbolic equations

D.-M. Cai; R. S. Falk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 6, page 667-698
  • ISSN: 0764-583X

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Cai, D.-M., and Falk, R. S.. "Reduced continuity finite element methods for first order scalar hyperbolic equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.6 (1994): 667-698. <http://eudml.org/doc/193755>.

@article{Cai1994,
author = {Cai, D.-M., Falk, R. S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {explicit finite element methods; first order linear hyperbolic problem; error estimates; convergence; numerical results; comparisons},
language = {eng},
number = {6},
pages = {667-698},
publisher = {Dunod},
title = {Reduced continuity finite element methods for first order scalar hyperbolic equations},
url = {http://eudml.org/doc/193755},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Cai, D.-M.
AU - Falk, R. S.
TI - Reduced continuity finite element methods for first order scalar hyperbolic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 6
SP - 667
EP - 698
LA - eng
KW - explicit finite element methods; first order linear hyperbolic problem; error estimates; convergence; numerical results; comparisons
UR - http://eudml.org/doc/193755
ER -

References

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  1. [1] D. CAI, Reduced continuity finite element methods for hyperbolic equations, Ph. D. Dissertation, Rutgers University, 1991. 
  2. [2] P. G. CIARLET, The Fintie Element Method for Elliptic Equations, North-Holland, Amsterdam, 1978. MR520174
  3. [3] R. S. FALK and G. R. RICHTER, Analysis of a continuous fimte element method for hyperbolic equations, SIAM J. Numer. Anal., 24 (1987), pp. 257-278. Zbl0619.65100MR881364
  4. [4] R. S. FALK and G. R. RICHTER, Local estimates for a finite element method for hyperbolic and convection-diffusion equations, SIAM J. Numer. Anal., 29 (1992), pp. 730-754. Zbl0757.65104MR1163354
  5. [5] M. FORTIN and M. SOULIE, A non-conforming piecewise quadratic finite element on triangles, Internat. J. Numer. Methods Engrg, 19 (1983), pp. 505-520. Zbl0514.73068MR702056
  6. [6] T. J. R. HUGHES and A. BROOKS, A multidimensional upwind scheme with no crosswind diffusion, in Finite Element Methods for Convection Dominated Flows (T. J. R. Hughes, ed.), AMD (ASME), 1979, pp. 19-35. Zbl0423.76067MR571681
  7. [7] C. JOHNSON, U. NÄVERT and J. PITKÄRANTA, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg, 45 (1984), pp. 285-312. Zbl0526.76087MR759811
  8. [8] C. JOHNSON and J. PITKÄRANTA, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp., 46 (1986), pp. 1-26. Zbl0618.65105MR815828
  9. [9] P. LESAINT and P. A. RAVIART, On a finite element method for solving the neutron transport equations, in Mathematical Aspects of Finite Elements in Partial Differential Equations (C. de Boor), ed.), Academis Press, New York, 1974, pp. 89-123. Zbl0341.65076MR658142
  10. [10] W. H. REED and T. R. HILL, Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory, Report LA-UR-73-479 (1973). 
  11. [11] G. R. RICHTER, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp., 50 (1988), pp. 75-88. Zbl0643.65059MR917819
  12. [12] R. WINTHER, A stable finite element method for first-order hyperbolic systems, Math. Comp., 36 (1981), pp. 65-86. Zbl0462.65066MR595042

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