Micro Abstract We present a new and completely parallel approach for fluid-structure interaction, which includes also contact between the elastic structures. Our approach is inspired by the fictitious domain method and makes intensive use of variational transfer between the solid and the fluid and on the possibly contacting surfaces between solids. We present the discretization, the setup of th...

This work deals with a posteriori error estimates for the obstacle problem. Deriving an estimator on the basis of the variational inequality with respect to the primal variable, an inconsistent one is obtained. To achieve consistency, this problem is treated by a Lagrange formalism, which transfers the variational inequality into a saddle point problem. Different techniques to ensure the stabil...

Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems.

In this paper we generalize the degenerate two{phase Stefan problem (Mullins{ Sekerka evolution) to multi{phase systems. We prove a conditional existence result for this evolution problem in the framework of geometric measure theory by using an implicit time discretization. In each time step we solve a variational problem for an energy functional that contains capillarity terms as well as bulk ...

The aim of this paper is to demonstrate the mathematical problems of modelling the physical process of heat and moisture transfer in porous materials. The method of discretization in time is applied to derive a discretized (generally non{potential) system of PDEs of elliptic type from the original variational problem of evolution. The convergence of corresponding Rothe sequences is studied.

Starting from a continuous congested traffic framework recently introduced in [8], we present a consistent numerical scheme to compute equilibrium metrics. We show that equilibrium metric is the solution of a variational problem involving geodesic distances. Our discretization scheme is based on the Fast Marching Method. Convergence is proved via a Γ-convergence result and numerical results are...

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods.

This chapter investigates the relationship between Routh symmetry reduction and time discretization for Lagrangian systems. Within the framework of discrete variational mechanics, a discrete Routh reduction theory is constructed for the case of abelian group actions, and extended to systems with constraints and non-conservative forcing or dissipation. Variational Runge–Kutta discretizations are...

We introduce a new variational time discretization for the system of isentropic Euler equations. In each timestep the internal energy is reduced as much as possible, subject to a constraint imposed by a new cost functional that measures the deviation of particles from their characteristic paths.

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [1], the discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macro-particles of arbitrary shape and discretization of field quanti...