This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This...

This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves $\Gamma \left(t\right):S\to {ℝ}^2$, $t\geqq 0$. The curves are driven by the normal velocity $v$ which is the function of curvature $\kappa$ and the position. The evolution law reads as: $v=-\kappa +F$. The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...

The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation...