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A semi-Lagrangian mixed finite element method for advection–diffusion variational inequalities

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  • Tber, Moulay Hicham

Abstract

We present a computational methodology for solving advection–diffusion variational inequalities. Our method is based on a Lagrange–Galerkin technique which combines a discretization of the material derivative along particle trajectories with a mixed finite element method. An efficient primal–dual active-set algorithm is designed to solve the resulting saddle point complementarity system. The overall approach applies to both advection and diffusion-dominated problems, and its performance is demonstrated on numerical examples with known analytical solutions and a benchmark from the literature.

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  • Tber, Moulay Hicham, 2023. "A semi-Lagrangian mixed finite element method for advection–diffusion variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 202-215.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:202-215
    DOI: 10.1016/j.matcom.2022.08.006
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Todd S. Munson & Francisco Facchinei & Michael C. Ferris & Andreas Fischer & Christian Kanzow, 2001. "The Semismooth Algorithm for Large Scale Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 294-311, November.
    3. Tinne Haentjens & Karel J. in 't Hout, 2015. "ADI Schemes for Pricing American Options under the Heston Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 207-237, July.
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    Cited by:

    1. Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.

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