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...

In this work, we show quasi-optimal interface error estimates for solutions obtained by the symmetric interior penalty discontinuous Galerkin method. It is proved that the numerical solution restricted to an interface converges with order |lnh|h under suitable regularity requirements, where the logarithmic factor is only present in the lowest order case, i.e., k = 1. For this case, we also deri...

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity...

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...

This article proposes a distributed algorithm for network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained as unconstrained smooth (continuously differentiable) exact penalty function. Computing gradient this in way challenging even under separability assumptions problem....

We consider region of interest (ROI) tomography of piecewise constant functions. We prove that continuous ROI data determine piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted `p–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We p...

We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positive...