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A modified Galerkin procedure with Hermite cubics for hyperbolic problems

Author: Lars Wahlbin
Journal: Math. Comp. 29 (1975), 978-984
MSC: Primary 65N30
MathSciNet review: 0388809
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Abstract: The Galerkin method, modified to include a term of artificial viscosity type, is applied to model problems for linear and quasilinear hyperbolic systems. Asymptotic error estimates are derived.

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  • [1] J. E. Dendy, Two methods of Galerkin type achieving optimum 𝐿² rates of convergence for first order hyperbolics, SIAM J. Numer. Anal. 11 (1974), 637–653. MR 0353695
  • [2] Todd Dupont, Galerkin methods for first order hyperbolics: an example, SIAM J. Numer. Anal. 10 (1973), 890–899. MR 0349046
  • [3] Todd Dupont, Galerkin methods for modeling gas pipelines, Constructive and computational methods for differential and integral equations (Sympos., Indiana Univ., Bloomington, Ind., 1974) Springer, Berlin, 1974, pp. 112–130. Lecture Notes in Math., Vol. 430. MR 0502035
  • [4] Lars B. Wahlbin, A dissipative Galerkin method applied to some quasilinear hyperbolic equations, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 109–117 (English, with Loose French summary). MR 0368447

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Article copyright: © Copyright 1975 American Mathematical Society