In this work, we study a unilateral contact problem with non local friction of Coulombbetween a locking material and a rigid foundation. In the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. In the second step, usingthe penalty method we...

We propose a $${\mathcal {C}}^0$$ interior penalty method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as simplified case. Standard high-order finite element approximations, nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in elements, plus integrals on mesh faces (sides 2D), that impos...

We give an error analysis of the finite element variable penalty method for Stokes equations. It is shown that the variable penalty method is of higher order than the standard penalty method.

where f ∈ L2(Ω). Let Th be a simplicial or convex quadrilateral triangulation of Ω. In C 0 interior penalty methods, we choose the discrete space Vh ⊂ H 1 0 (Ω) to be either a P` (` ≥ 2) triangular Lagrange finite element space or a Q` (` ≥ 2) tensor product finite element space associated with Th. By an integration by parts argument [4], it can be shown that the solution u of (1), which belong...

We study stabilization methods for the discretization of convection-dominated elliptic convection-diffusion problems by linear finite elements. It turns out that there exist close relations between a new version of stabilization via local projection and the continuous interior penalty method. AMS Subject Classifications: 65 N15, 65N30, 65N12