Convergence of a shock-capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions

Mathematics of Computation

Volumn 53, Issue 188, 1989, Pages 527-545

  Szepessy, Anders ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968514036     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1989-0979941-6     Document Type: Article

References (11)

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2. T. J. R. HUGHES & M. Mallet, “A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, ” Comput. Methods Appl. Mech. Engrg., v. 58, 1986, pp. 329-336.
3. T. J. R. HUGHES, L. P. FRANCA & M. MALLET, “VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multidimensional advective-diffusive systems, ” Comput. Methods Appl. Mech. Engrg., v. 63, 1987, pp. 97-112.
4. C. JOHNSON, U. NÄVERT & J. Pitkaranta, “Finite element methods for linear hyperbolic problems, ” Comput. Methods Appl. Mech. Engrg., v. 45, 1984, pp. 285-312.
5. C. JOHNSON & J. SARANEN, “Streamline diffusion methods for problems in fluid mechanics, ” Math. Comp., v. 47, 1986, pp. 1-18.
6. C. JOHNSON & A. Szepessy, “On the convergence of a finite element method for a nonlinear hyperbolic conservation law, ” Math. Comp., v. 49, 1987, pp. 427-444.
7. C. JOHNSON, A. Szepessy & P. HANSBO, On the Convergence of Shock-Capturing Streamline Diffusion Finite Element Methods for Hyperbolic Conservation Laws, Preprint No 1987:21, Dept, of Math., Chalmers Univ. of Technology, S-412 96 Göteborg. (To appear in Math. Comp.)
8. S. N. KRUZKOV, “First order quasilinear equations in several independent variables, ” Math. USSR-Sb., v. 10, 1970, pp. 217-243.
9. A. SZEPESSY, “Measure-valued solutions of scalar conservation laws with boundary conditions, ” Arch. Rational Mech. Anal. (To appear.)
10. L. TARTAR, Compensated Compactness and Applications to Partial Differential Equations, in Research Notes in Mathematics, Nonlinear Analysis and Mechanics: Heriot-Watts Symposium, vol. 4 (R. J. Knops, ed.), Pitman Press, London, 1979.
11. L. TARTAR, The Compensated Compactness Method Applied to Systems of Conservation Laws, Systems of Nonlinear Partial Differential Equations (J. M. Ball, ed.), NATO ASI series, Reidel, Dordrecht, 1983, pp. 263 285.