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Titlebook: Partial Differential Equations; Modelling and Numeri Roland Glowinski,Pekka Neittaanmäki Book 2008 Springer Science+Business Media B.V. 200

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Computing the Eigenvalues of the Laplace-Beltrami Operator on the Surface of a Torus: A Numerical Approachb which is based upon ARPACK. We show results for problems of order 16K variables where we computed lowest 15 modes. We also show a bifurcation study of eigenvalue trajectories as functions of aspect ration of the major to minor axis of the torus.
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Calibration of Lévy Processes with American Optionsthe state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.
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Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equationsquation on meshes with mixed cells when all the coefficients and the source function may have discontinuities inside polyhedral mesh cells. The resulting discrete equations operate only with the degrees of freedom for normal fluxes on the boundaries of cells and one degree of freedom per cell for th
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A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficientso subdomains and use explicit time difference scheme along with piecewise linear finite element approximations on semimatching grids. We apply boundary supported Lagrange multiplier method to match the solution on the interface between subdomains. The resulting system of linear equations of the “sad
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