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The comparison between two mortar spectral element methods for Darcy’s equations

Abstract : We mainly talk about in this thesis the numerical simulation of the steady flow in a rigid porous medium which is simulated by Darcy's equations with general boundary conditions, by spectral method. The method has been proven optimal in the sense that the order of convergence is only limited by the regularity of the solution. One of the parameters of the system depends on the permeability of the medium and, when this one is not homogeneous, the variations of the parameter could be very high. To handle this phenomenon, we propose two different discretization relies on the mortar spectral method. Both the numerical analysis of the discretization problems are performed and numerical experiments are presented, which turn out to be in good coherency with the theoretical results. In addition, we develop a Legendre Petrov-Galekin method for linear fourth-order differential equations in one dimension and Legendre Petrov-Galerkin and Chebyshev collocation method for the nonlinear Kuramoto-Sivashinsky equation. The numerical experiments are given which demonstrate the efficient of proposed schemes. Finally, we give the optimal rate of convergence [...]
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Submitted on : Friday, July 17, 2020 - 12:35:10 PM
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Kangzheng Xing. The comparison between two mortar spectral element methods for Darcy’s equations. Spectral Theory [math.SP]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066740⟩. ⟨tel-02901567⟩



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