A posteriori error estimation and adaptivity in the method of lines with mixed finite elements

Brandts, Jan

doi:10.1023/a:1022268703907

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“…The adaptive scheme for one dimensional boundary value problems is studied in 1984 by Babuska et.al [3]. Studies about adaptive schemes with mixed finite element methods have been carried out in [4]- [7], [10] and the references therein. Details on the theory of adaptive finite element methods can be referred to [8].…”

Section: Introductionmentioning

confidence: 99%

Numerical Studies: Adaptive Mixed Finite Element Schemes for Benjamin-Bona-Mahony and Burgers Equations

Shafie¹,

Tran²

2020

IJETT

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Adaptive mixed finite element schemes for Benjamin-Bona-Mahony and Burgers equations are considered. The aim is to generate more accurate approximate solutions of the exact solution and its derivative by using adaptive mesh refinement scheme. The mesh is refined by using two proposed methods with selected tolerance to achieve approximate solutions having specified accuracy in an optimal way. The computation begins with an experimental set of approximate solutions generated on a coarse initial mesh by using the mixed finite element method. Then, the error estimate of these solutions is appraised. A principal tool of this adaptive scheme is the availability of local error estimates, namely local a posteriori error estimators. The numerical results show that the desired accuracy of approximate solution can be accomplished by using the proposed adaptive schemes.

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