A posteriori error estimates and adaptive finite elements for a nonlinear parabolic problem related to solidification |
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| Affiliation: | 1. Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland;2. Institut Elie Cartan, Universite Henri Poincare Nancy 1, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France;1. Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil;2. Departamento de Matemática, Universidade Federal de Ouro Preto, ICEB, 35400-000, Ouro Preto, MG, Brazil;1. Department of Law and Economics, University Mediterranea of Reggio Calabria, Via dei Bianchi, 2 – 89127 Reggio Calabria, Italy;2. Department of Basic Sciences, Babol (Noushirvani) University of Technology, Babol, Iran;3. Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran;1. Eindhoven University of Technology, Multiscale Engineering Fluid Dynamics, 5600 MB Eindhoven, Netherlands;2. School of Mathematical Sciences, The University of Nottingham University Park, Nottingham NG7 2RD, United Kingdom |
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| Abstract: | A posteriori error estimates are derived for a nonlinear parabolic problem arising from the isothermal solidification of a binary alloy. Space discretization with continuous, piecewise linear finite elements is considered. The L2 in time H1 in space error is bounded above and below by an error estimator based on the equation residual. Numerical results show that the effectivity index is close to one. An adaptive finite element algorithm is proposed and a solutal dendrite is computed. |
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