A parallel element-by-element ,nultilevel strategy is developed and applied to two nonlinear, coupled PDE system.•. Spectral (p) finite elements are used to discretize the lems and the multilevel solution strategy uses projections between bases of different degree (level). The projection methods for the p-multilevel schemes are developed and analyzed for Lagrange and hierarchic bases. The appro...

The paper is concerned with a methodology of optimal design of shells of minimum weight with strength, stability and strain constraints. Stress and strain state of the shell is determined by Galerkin method in the mixed finite element formulation within the geometrically nonlinear theory. The analysis of the effectiveness of different optimization algorithms to solve the set problem is given. T...

A dual-parametric finite element method is introduced in this paper for the computation of singular minimizers in the two dimensional cavitation problem in nonlinear elasticity. The method overcomes the difficulties, such as the mesh entanglement and material interpenetration, generally encountered in the finite element approximation of problems with extremely large expansionary deformation. Nu...

A finite-element approach combined with an efficient iterative method have been used to provide a numerical solution of the nonlinear Poisson-Boltzmann equation. The iterative method solves the nonlinear equations arising from the FE discretization procedure by a node-by-node calculation. The performance of the proposed method is illustrated by applying it to the problem of two identical colloi...

In this article, we propose and analyse a combined finite volume–finite element scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions without imposing any restrictions on the mesh. Moreover, following the work of C. Cancès et al. 2013, we define a nonlinear correction of the diffusive terms to obtain a monotone scheme. We provide, unde...

We study a finite volume element discretization of a nonlinear parabolic equation in a convex polygonal domain. We show existence of the discrete solution and derive error estimates in L2– and H –norms. We also consider a linearized method and provide numerical results to illustrate our theoretical findings.

In this paper, a nonlinear control volume finite element (CVFE) scheme for a degenerate Keller– Segel model with anisotropic and heterogeneous diffusion tensors is proposed and analyzed. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in finite element methods. The diffusion term which involves an anisotropic and heterogeneous tensor is discretized on...

the paper is concerned with a methodology of optimal design of shells of minimum weight with strength, stability and strain constraints. stress and strain state of the shell is determined by galerkin method in the mixed finite element formulation within the geometrically nonlinear theory. the analysis of the effectiveness of different optimization algorithms to solve the set problem is given. t...

Abstract. We consider a nonlinear system of elliptic equations, which arises when modelling the heat diffusion problem coupled with the electrical diffusion problem. The ohmic losses which appear as a source term in the heat diffusion equation yield a nonlinear term which couples both equations. A finite element scheme and a finite volume scheme are considered for the discretization of the syst...