Analysis of Finite Element Methods for Linear Hyperbolic Problems

  • Richard S. Falk
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)


We summarize several techniques of analysis for finite element methods for linear hyperbolic problems, illustrating their key properties on the simplest model problem. These include the discontinuous Galerkin method, the continuous Galerkin methods on rectangles and triangles, and a nonconforming linear finite element on a special triangular mesh.


Finite Element Method Galerkin Method Discontinuous Galerkin Method Triangle Edge Neutron Transport Equation 
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  1. 1.
    Cai, D-M.: Reduced continuity finite element methods for hyperbolic equations. Ph.D. Dissertation, Rutgers University, (1991)Google Scholar
  2. 2.
    Falk, R.S., Richter, G.R.: Analysis of a continuous finite element method for hyperbolic equations. SIAM J. Numer. Anal. 24 (1987) 257–278MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Falk, R.S., Richter, G.R.: Local estimates for a finite element method for hyperbolic and convection-diffusion equations. SIAM J. Numer. Anal. 29 (1992) 730–754MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Johnson, C., Pitkâranta, J.: An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comp. 46 (1986) 1–26MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Lesaint, P., Raviart, P-A.: On a finite element method for solving the neutron transport equation. Mathematical Aspects of Finite Elements in Partial Differential Equations, (C. de Boor, ed.), Academic Press, New York, (1974) 89–123Google Scholar
  6. 6.
    Reed, W. H., Hill, T. R.: Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory Technical Report LA-UR-73–479 (1973)Google Scholar
  7. 7.
    Winther, R.: A stable finite element method for first-order hyperbolic systems. Math. Comp. 36 (1981) 65–86MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Richard S. Falk
    • 1
  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA

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