Improved least-squares error estimates for scalar hyperbolic problems (Q2726277)
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scientific article; zbMATH DE number 1620718
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improved least-squares error estimates for scalar hyperbolic problems |
scientific article; zbMATH DE number 1620718 |
Statements
1 August 2001
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advection-convection equation
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hyperbolic equations
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error estimates
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finite element methods
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least squares method
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Improved least-squares error estimates for scalar hyperbolic problems (English)
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The authors consider a \(L^2\)-norm least squares principle for a scalar hyperbolic problem.Optimal errors with zero gap typically arise in the context of elliptic equations, while finite element methods for hyperbolic problems tend to produce approximations with a positive gap [see \textit{C. Johnson, U. Nävert} and \textit{J. Pitkäranta}, Comput. Methods Appl. Mech. Engineering 45, 285-312 (1984; Zbl 0537.76060)]. For rectangular domains and constant advection in one of the coordinate directions,the authors are able to improve the gap of the least squares method to 2/3.
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