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UPSI Digital Repository (UDRep)
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| Abstract : |
| Error estimations of H1 mixed finite element method for the Benjamin-Bona-Mahony equation are considered. The problem is reformulated into a system of first order partial differential equations, which allows an approximation of the unknown function and its derivative. Local parabolic error estimates are introduced to approximate the true errors from the computed solutions; the so-called a posteriori error estimates. Numerical experiments show that the a posteriori error estimates converge to the true errors of the problem. |
| References |
1. Pani, A.K. An H1-galerkin mixed finite element method for parabolic partial differential equations (1998) SIAM Journal on Numerical Analysis, 35 (2), pp. 712-727. Cited 63 times. http://epubs.siam.org/loi/sjnaam doi: 10.1137/S0036142995280808 2. Adjerid, S., Flaherty, J.E., Wang, Y.J. A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems (1993) Numerische Mathematik, 65 (1), pp. 1-21. Cited 33 times. doi: 10.1007/BF01385737 3. Shafie, S., Tran, T. Estimating the error of a H1 - Mixed finite element solution for the Burgers equation (2016) Proceedings of the 17th Biennial Computational Techniques and Applications Conference, CTAC-2014, 56, pp. C383-C398. 4. Tran, T., Duong, T.-B. A complete analysis for some a posteriori error estimates with the finite element method of lines for a nonlinear parabolic equation (2002) Numerical Functional Analysis and Optimization, 23 (7-8), pp. 891-909. doi: 10.1081/NFA-120016275 5. Tran, T., Duong, T.-B. A posteriori error estimates with the finite element method of lines for a sobolev equation (2005) Numerical Methods for Partial Differential Equations, 21 (3), pp. 521-535. Cited 6 times. doi: 10.1002/num.20045 |
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