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Mathematics of Computation

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A simplified Galerkin method for hyperbolic equations


Authors: R. C. Y. Chin, G. W. Hedstrom and K. E. Karlsson
Journal: Math. Comp. 33 (1979), 647-658
MSC: Primary 65M10; Secondary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1979-0521280-5
MathSciNet review: 521280
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Abstract: We modify a Galerkin method for nonlinear hyperbolic equations so that it becomes a simpler method of lines, which may be viewed as a collocation method. The high order of accuracy is preserved. We present a linear wave analysis of the scheme and discuss some aspects of nonlinear problems. Our numerical experiments indicate that the addition of a proper artificial viscosity makes the method competitive and the common difference schemes, even when the solution has discontinuities.


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DOI: https://doi.org/10.1090/S0025-5718-1979-0521280-5
Article copyright: © Copyright 1979 American Mathematical Society