1. A new low order least squares nonconforming characteristics mixed finite element method For Burgers’ equation.
- Author
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Shi, Dongyang, Zhou, Jiaquan, and Shi, Dongwei
- Subjects
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LEAST squares , *FINITE element method , *BURGERS' equation , *APPROXIMATION theory , *ERROR analysis in mathematics , *MATHEMATICAL variables , *INTERPOLATION - Abstract
Abstract: In this paper, a new low order least squares nonconforming characteristics mixed finite element method (MFEM) is considered for two-dimensional Burgers’ equation. By use of two typical characters of the elements for approximating the velocity and flux variables: (a) the consistency errors of the elements can be estimated as order with respect to the mesh size h in the broken -norm, one order higher than their interpolation errors; (b) the elements’ interpolation operators satisfy certain orthogonalities, which lead to order error estimates in -norm and some superclose results, the accuracy of corresponding variables in -norm is improved by one order compared with other MFEMs in the existing literature. It seems that the results provided herein have never been derived before. [Copyright &y& Elsevier]
- Published
- 2013
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