Convergence of the discrete free boundaries for finite element approximations

Convergence of the discrete free boundaries for finite element approximations

Convergence Analysis for Eigenvalue Approximations on Triangular Finite Element Meshes

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

Convergence of Finite Element Approximations of Large Eddy Motion

Fluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are solved numerically. This report considers ...

Monotone convergence of finite element approximations of obstacle problems

The purpose of the work is to study the monotone convergence of numerical solutions of obstacle problems under mesh 4 refinement when the obstacle is convex. We prove monotone convergence of piecewise linear finite element approximations for 5 one-dimensional obstacle problems. We demonstrate by giving a example that such monotone convergence will not hold in the 6 two-dimensional case. 7 c © 2...

Convergence of free boundaries in discrete obstacle problems

We show that a piecewise linear finite element approximation of the obstacle problem gives an approximate free boundary converges, in an appropriate distance, to the free boundary of the continuous problemunder a stability condition on the obstacle.