Papers by Abderrahman Issaoui
We consider a contact problem between an elastic body and a rigid foundation with Tresca’s fricti... more We consider a contact problem between an elastic body and a rigid foundation with Tresca’s friction law, present a hp-discretization technique of a mixed formulation based on biorthogonal basis functions and solve the corresponding discrete system with the semi-smooth Newton method. A-posteriori error estimates using an error indicator in an hp-adaptive refinement algorithm are derived. We show convergence of the hpversion of BEM and present some numerical experiments. Furthermore we consider a mixed boundary element formulation, which is stabilized following ideas of P.Hild, Y. Renard and V.Lleras for the FEM. A mesh-dependent stabilization term is added to the discrete mixed formulation, in order to avoid the discrete inf-sup condition. Existence and uniqueness of the solution of the discrete problem are shown together with a priori error and a posteriori error estimates. Numerical experiments are listed for the stabilized and the non-stabilized cases. A stochastic contact problem...
Numerische Mathematik, 2016
We investigate hp-stabilization for variational inequalities and boundary element methods based o... more We investigate hp-stabilization for variational inequalities and boundary element methods based on the approach introduced by Barbosa and Hughes for finite elements. Convergence of a stabilized mixed boundary element method is shown for unilateral frictional contact problems for the Lamé equation. Without stabilization, the inf-sup constant need not be bounded away from zero for natural discretizations, even for fixed h and p. Both a priori and a posteriori error estimates are presented in the case of Tresca friction, for discretizations based on Bernstein or Gauss-Lobatto-Lagrange polynomials as test and trial functions. We also consider an extension of the a posteriori estimate to Coulomb friction. Numerical experiments underline our theoretical results.
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Papers by Abderrahman Issaoui