Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity
This paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of...
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| Format: | Report |
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Unspecified
1996
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| Summary: | This paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of hyperbolic systems and scalar hyperbolic equations. We also consider the problem of a posteriori error estimation for linear functionals of the solution. The a posteriori error bounds are implemented into an adaptive finite element algorithm. |
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