# Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions

- Volume: 27, Issue: 1, page 55-63
- ISSN: 0764-583X

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topBales, L. A.. "Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.1 (1993): 55-63. <http://eudml.org/doc/193694>.

@article{Bales1993,

author = {Bales, L. A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {nonsmooth solutions; finite element; initial-boundary value problem; second order hyperbolic equation; semidiscrete approximations; fully discrete approximations; convergence estimates; negative norms},

language = {eng},

number = {1},

pages = {55-63},

publisher = {Dunod},

title = {Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions},

url = {http://eudml.org/doc/193694},

volume = {27},

year = {1993},

}

TY - JOUR

AU - Bales, L. A.

TI - Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 1993

PB - Dunod

VL - 27

IS - 1

SP - 55

EP - 63

LA - eng

KW - nonsmooth solutions; finite element; initial-boundary value problem; second order hyperbolic equation; semidiscrete approximations; fully discrete approximations; convergence estimates; negative norms

UR - http://eudml.org/doc/193694

ER -

## References

top- [1] G. A. BAKER and J. H. BRAMBLESemidiscrete and single step fully discrete approximations for second order hyperbolic equations, RAIRO Modél. Math. Anal. Numer., V. 13, 1979, pp. 75-100. Zbl0405.65057MR533876
- [2] L. A. BALES, Finite element computations for second order hyperbolic equations with nonsmooth solutions, Comm. in App. Num. Meth., V. 5, 1989, pp. 383-388. Zbl0679.65086
- [3] J. H. BRAMBLE and A. H. SCHATZ, Higher order local accuracy by averaging in the finite element method, Math. Comp., V. 31, 1977, pp. 94-111. Zbl0353.65064MR431744
- [4] T. GEVECI, On the convergence of Galerkin approximation schemas for second-order hyperbolic equations in energy and negative norms, Math. Comp., V. 42, 1984, pp.393-415. Zbl0553.65082MR736443
- [5] C. JOHNSON and U. NAVERT, An analysis of some finite element methods for advection-diffusion problems, in Analytical and Numerical Approaches to Asymptotic Problems in Analysis, L. S. Frank and A. van der Sluis (Eds), North-Holland, 1981, pp. 99-116. Zbl0455.76081MR605502
- [6] P. D. LAX and M. S. MOCK, The computation of discontinuous solutions of linear hyperbolic equations, Comm Pure Appl. Math., V. 31, 1978, pp. 423-430. Zbl0362.65075MR468216
- [7] V. THOMEE, Galerkin Finite Methods for Parabolic Problems, Springer-Verlag, 1984. Zbl0528.65052MR744045

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