0000000001335862
AUTHOR
Neittaanmäki, P.
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
The tradìtíonal splitting-up method or fractíonal step method is stuítable for sequentìal compulìng. Thís means that the computing of the present fractional step needs the value of the previous fractional steps. In thìs paper we propose a new splitting-up scheme for which the computing of the fractional steps is índependent of each other and therefore can be computed by parallel processors. We have proved the convergence estimates of this scheme both for steady state and nonsteady state linear and nonlinear problems. To use .finite element method to solve Navier-Stokes problems it is always dfficult to handle the zero-divergent finíte element spaces. Here, by using the splitting-up method w…