In this study, we implement a variant of infeasible interior-point algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the LCP as an minimization problem. Then descent iterative method is applied to latter. The direction computed via Newton method. However, maintaining positivity iterates, novel and efficient strategy proposed. Some numerical results are r...

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...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

In this paper we are concerned with the computation of a liquid crystal model defined by a simplified Oseen-Frank energy functional and a (sphere) nonlinear constraint. A particular case of this model defines the well known harmonic maps. We design an new iterative method for solving such a minimization problem with the nonlinear constraint. The main ideas are to linearize the nonlinear constra...

The paper presents an algorithm of adaptation by successive mesh regeneration and its application to the potential nonlinear flow problems. The Newton-Raphson method is applied to the solution of nonlinear problem. The Kutta-Zhukovsky condition is implemented by the penalty function method. The adaptation algorithm is based on the modification of mesh size function depending on the error indica...

In this article, we study a class of evolution variational inequalities with p(x, t)-growth conditions on bounded domains. By means of the penalty method and Galerkin’s approximation, we obtain the existence of weak solutions. Moreover, the boundedness of weak solutions is also investigated by applying Moser’s iterative method.

In this talk we will discuss several two-level additive Schwarz preconditioners for a weakly over-penalized symmetric interior penalty (WOPSIP) method. The WOPSIP method belongs to the family of discontinuous finite element methods. Theoretical results on the condition number estimate of the preconditioned system will be presented along with numerical results. THE DISCRETE PROBLEM Let Ω be a bo...

The aim of this work is to propose a new numerical method for solving the mechanical frictional contact problem in the general case of multi-bodies in a three dimensional space. This method is called adapted augmented Lagrangian method (AALM) and can be used in a multi-physical context (like thermo-electro-mechanical fields problems). This paper presents this new method and its advantages over ...