Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries

The aim of this paper is to establish the convergence and error bounds to the fully discrete solution for a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite elements methods are investigated

Time-Dependent Fluid-Structure Interaction

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure which reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM

Véges rugalmas-képlékeny alakváltozás elméleti és numerikus vizsgálata = Theoretical and numerical investigation of finite elasto-plastic deformation

Az OTKA kutatási téma keretében az alábbi kutatási eredmények születtek: -A mikropoláris testek rugalmas-képlékeny alakváltozásának számítására végelemes eljárás dolgoztunk ki háromdimenziós testek és és kis alakváltozások esetén. -A Mises-féle képlékenységi feltételt kiterjesztettük a mikropoláris anyagokra, a rugalmas torzítási energia alapján. -A kétdimenziós rugalmasságtani feladatok és a peridynamikus modell számítására meshless eljáráson alapuló program kidolgására került sor. -A Prandtl-Reuss modell anyagegyenleteinek integrálására egzakt eljárásokat dolgoztunk ki lineárisan keményedő modellek esetén. -Egykristályok véges rugalmas-képlékeny alakváltozára javasolt modellekben a rugalmas alakváltozás leírására vonatkozó anyagegyenleteket elemeztük különböző csúszási rendszerek esetén | The research work within in the present OTKA can be summarized as follows: -A 3D finite elment program was developed for micropolar elastoplasticity at small deformations. -The classical Mises yield function has been extended to micropolar solids based on elastic distorsional energy. -The nonlocal peridynamic material model was analysed by the meshless method. and a two dimesional computer code was developed -A new exact integration method for Prandtl-Reuss model with linear isotropic-kinematic hardening has been presented. -The constitutive relations of single crystal elastoplasticity was investigated, and its elastic model was analysed by different test examples (one and two slips system