The convergence of the finite element solution for the second order elliptic problem in the -dimensional bounded domain with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the and norms are obtained.
The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.
The linear stability problem of inviscid incompressible steady flow between two concentric cylinders is investigated. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem for linearized Euler equations. The discrete eigenvalue problem is obtained by the spectral element method. The algorithm is implemented in MATLAB. The developed program serves as a simple tool for numerical experimenting. It enables to state rough dependency of the stability on various...
Page 1