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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
MathSciNet review: 1122082
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Abstract: Finite element approximations of the first-order hyperbolic equation ${\mathbf {U}} \bullet \nabla u + \alpha u = f$ are considered on curved domains $\Omega \subset {\mathbb {R}^2}$. When part of the boundary of $\Omega$ is characteristic, the boundary of numerical domain, ${\Omega _h}$, 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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Keywords: Hyperbolic equations, nonconforming approximation
Article copyright: © Copyright 1992 American Mathematical Society