Numerical solutions of cascade flows by finite element method [Abstract of thesis]
Výpočtová matematika a počítačová dynamika tekutin
Finite element solution of flows through cascades of profiles in a layer of variable thickness
The paper is devoted to the numerical modelling of a subsonic irrotational nonviscous flow past a cascade of profiles in a variable thickness fluid layer. It leads to a nonlinear two-dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The problem is discretized by the finite element method. Both theoretical and practical questions of the finite element implementation are studied; convergence of the method, numerical integration, iterative methods for the solution of...
Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems
The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the and error estimates are established. At the end...
Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems
We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly...
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