In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely the enrichment of the solution field via the definition of overl...

Degrees of freedom which are Lagrange multipliers anse in the finite element approximation of mixed vanational problems. When these degrees of freedom are "local", the intioduction of a small perturbation {conespondinq hv duality to a penalty function) enables the élimination of these unknouns at the element level We fitst examine this method in the continuons case and show that the solution of...

We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the penalty parameter tends to infinity. We apply this result to equations of non-negative characteristic form and the non-linear, time dependent system of incompressible miscible displacement. Moreover, we investigate varyi...

In the present work, we investigate mathematical and numerical aspects of interior penalty finite element methods for free surface flows. We consider the incompressible Navier-Stokes equations with variable density and viscosity, combined with a front capturing model using the level set method. We formulate interior penalty finite element methods for both the Navier-Stokes equations and the lev...

A Posteriori Error Analysis in the maximum norm for a penalty finite element method for the time-dependent obstacle problem Abstract. We consider nite element approximation of the parabolic obstacle problem. The analysis is based on a penalty formulation of the problem where the penalisation parameter is allowed to vary in space and time. We estimate the penalisation error in terms of the penal...