DD-type Domain Decomposition Method for Frictional Contact Problem

Abstract

The bilateral or unilateral contact problem with Coulomb friction between two elastic bodies is considered [1]. An algorithm is introduced to solve the resulting finite element system by a non-overlapping domain decomposition method. The global problem is transformed to a smaller problem on the contact surface. The solution is obtained by using a successive approximation method, in each step of this algorithm we solve two intermediate problems the first with prescribed tangential pressure and the second with prescribed normal pressure.

Implicit Extension of Taylor Series Method with Numerical Derivatives

“…we have shown the truncated Taylor's series for two subintervals generated by algorithm with automatic error control. The implicit Taylor series method with numerical derivatives proposed in this article gives continuously differentiable piecewise polynomials function as approximate solution and because its numerical-analytical character can be applied for solving qualitative problems too [4].…”