A Family of Higher Order Mixed Finite Element Methods for Plane Elasticity.
Analysis of a quasicontinuum method in one dimension
The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range interactions and a QC formulation which incorporates several important aspects of practical QC methods. First, we prove the existence, the local uniqueness...
Application of the matrix algebra to contact problems in railways
Approximation and numerical solution of contact problems with friction
The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function on a certain convex set . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.