# Journals and Conference Proceedings

Permanent URI for this communityhttps://hdl.handle.net/10877/136

Academic publications and conference proceedings from members of the university community.

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# Browsing Journals and Conference Proceedings by Author "Abdelwahed, Mohamed"

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Item A stabilized finite element method for Stream function vorticity formulation of Navier-Stokes equations(Texas State University, Department of Mathematics, 2017-01-19) Abdelwahed, Mohamed; Chorfi, Nejmeddine; Hassine, MaatougWe the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numerical algorithm is presented and tested.Item Approximation of the leading singular coefficient of an elliptic fourth-order equation(Texas State University, Department of Mathematics, 2017-12-14) Abdelwahed, Mohamed; Chorfi, Nejmeddine; Radulescu, VicentiuThe solution of the biharmonic equation with an homogeneous boundary conditions is decomposed into a regular part and a singular one. The later is written as a coefficient multiplied by the first singular function associated to the bilaplacian operator. In this paper, we consider the dual singular method for finding the value of the leading singular coefficient, and we use the mortar domain decomposition technique with the spectral discretization for its approximation. The numerical analysis leads to optimal error estimates. We present some numerical results which are in perfect coherence with the analysis developed in this paper.Item Asymptotic formula for detecting inclusions via boundary measurements(Texas State University, Department of Mathematics, 2018-06-28) Khelifi, Khalifa; Abdelwahed, Mohamed; Chorfi, Nejmeddine; Hassine, MaatougIn this article, we are concerned with a geometric inverse problem related to the Laplace operator in a three-dimensional domain. The aim is to derive an asymptotic formula for detecting an inclusion via boundary measurement. The topological sensitivity method is applied to calculate a high-order topological asymptotic expansion of the semi-norm Kohn-Vogelius functional, when a Dirichlet perturbation is introduced in the initial domain.Item Determination of obstacles in Stokes flow by boundary measurement(Texas State University, Department of Mathematics, 2017-09-25) Abdelwahed, Mohamed; Barhoumi, Montassar; Chorfi, NejmeddineWe study the determination of some obstacles in a Stokes flow domain with overdetermined boundary data. We use a method based on the topological sensitivity technique associated to the reciprocity gap function concept. We develop an asymptotic formula between the flow parameters and the boundary data. The obtained formula is interesting and serve as a useful tool to develop an accurate and robust numerical method in geometry inverse problems.Item Handling geometric singularities by the mortar spectral element method for fourth-order problems(Texas State University, Department of Mathematics, 2017-03-24) Abdelwahed, Mohamed; Chorfi, Nejmeddine; Radulescu, VicentiuThis article concerns the numerical analysis and the error estimate of the biharmonic problem with homogeneous boundary conditions using the mortar spectral element method in domains with corners. Since the solution of this problem can be written as a sum of a regular part and known singular functions, we propose to use the Strang and Fix algorithm for improving the order of the error.Item Numerical solutions to heat equations via the spectral method(Texas State University, Department of Mathematics, 2016-03-11) Abdelwahed, Mohamed; Chorfi, Nejmeddine; Radulescu, VicentiuIn this article we study a discretized version of the heat equation. For the time semi-discrete problem, we use an implicit Euler's scheme, and for the space discretization we used the spectral method. We estimate for the error between the exact and approximated discrete solutions, and illustrate the features of our method with numerical examples.