Numerical methods for unilateral problems

Numerical Methods for Multiscale Problems

[2] J. Bourgain, Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Geometric and Functional Analysis 3 (1993), 107–156. [3] M. Christ, J. Colliander and T. Tao, Instability of the periodic nonlinear Schrödinger equation, Preprint, 2003. [4] M. Hochbruck, A. Ostermann, Explicit exponential Runge-Kutta methods for semilinear par...

Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error esti...

A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis

We introduce a Nitsche-based formulation for the finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the non-linear contact conditions through a consistent penalty term. Without any additional assumption on the contact set, we can prove theoretically its fully optimal convergence rate in the H(Ω)norm for linear finite elements in...

Numerical Methods for Power-Law Diffusion Problems

Numerical Methods for Scalar Convection-Dominated Problems