Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach

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• 作者：Grigori Chapiro ; Angel E. R. Gutierrez…
• 关键词：Moving boundary problems ; Nonlinear complementarity algorithms ; Combustion ; Diffusion ; 35R37 ; 90C33 ; 80A25
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：168
• 期：2
• 页码：534-550
• 全文大小：772 KB
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• 作者单位：Grigori Chapiro (1)
  Angel E. R. Gutierrez (2)
  José Herskovits (3) (4)
  Sandro R. Mazorche (1)
  Weslley S. Pereira (1)
  
  1. Department of Mathematics, Federal University of Juiz de Fora, Juiz de Fora, Brazil
  2. Instituto de Matemática y Ciencias Afines (IMCA), Lima, Peru
  3. Department of Mechanical and Materials Engineering, Military Institute of Engineering, Rio de Janeiro, Brazil
  4. Mechanical Engineering Program, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

Parabolic-type problems, involving a variational complementarity formulation, arise in mathematical models of several applications in Engineering, Economy, Biology and different branches of Physics. These kinds of problems present several analytical and numerical difficulties related, for example, to time evolution and a moving boundary. We present a numerical method that employs a global convergent nonlinear complementarity algorithm for solving a discretized problem at each time step. Space discretization was implemented using both the finite difference implicit scheme and the finite element method. This method is robust and efficient. Although the present method is general, at this stage we only apply it to two one-dimensional examples. One of them involves a parabolic partial differential equation that describes oxygen diffusion problem inside one cell. The second one corresponds to a system of nonlinear differential equations describing an in situ combustion model. Both models are rewritten in the quasi-variational form involving moving boundaries. The numerical results show good agreement when compared to direct numerical simulations. Keywords Moving boundary problems Nonlinear complementarity algorithms Combustion Diffusion