Malaysian Journal of Mathematical Sciences, January 2019, Vol. 13, No. 1
A Mixed Formulation in Conjunction with the Penalization Method for Solving the Bilaplacian Problem with Obstacle Type Constraints
Hannache, A., Laouar, A., and Sissaoui, H.
Corresponding Email: abdelhamid.laouar@univ-annaba.dz
Received date: 2 June 2018
Accepted date: 4 January 2019
Abstract:
In this paper, we consider a mixed formulation for the study of the bilaplacian problem with obstacle constraints in conjunction with the penalization method. The idea is based on the decomposition of the bilaplacian operator into two coupled laplacians and of course by choosing suitable spaces. The numerical advantage is to allow the solution of coupled systems with nice matrices having the M-matrix property. Moreover, the computed solution of the problem requires less execution time with respect to the discrete system of the bilaplacian problem. For simulation, we test the efficiency of a variety of iterative relaxation methods and discuss their numerical performances.
Keywords: Mixed formulation, Unilateral constraint, Bilaplacian problem, Method of penalization
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