Convergence of nonconforming finite element approximations to first-order linear hyperbolic equations

Author:
Noel J. Walkington

Journal:
Math. Comp. **58** (1992), 671-691

MSC:
Primary 65N30; Secondary 65M60, 76M10

DOI:
https://doi.org/10.1090/S0025-5718-1992-1122082-8

MathSciNet review:
1122082

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Abstract: Finite element approximations of the first-order hyperbolic equation are considered on curved domains . When part of the boundary of is characteristic, the boundary of numerical domain, , may become either an inflow or outflow boundary, so it is necessary to select an algorithm that will accommodate this ambiguity.

This problem was motivated by a problem in acoustics, where an equation similar to the one above is coupled to three elliptic equations. In the last section, the acoustics problem is briefly recalled and our results for the first-order equation are used to demonstrate convergence of finite element approximations of the acoustics problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1992-1122082-8

Keywords:
Hyperbolic equations,
nonconforming approximation

Article copyright:
© Copyright 1992
American Mathematical Society