An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains

An Adaptive Finite Element Method for the Incompressible Navier{stokes Equations on Time-dependent Domains

Finite element methods for the Stokes problem on complicated domains

It is a standard assumption in the error analysis of finite element methods that the underlying finite element mesh has to resolve the physical domain of the modeled process. In case of complicated domains appearing in many applications such as ground water flows this requirement sometimes becomes a bottleneck. The resolution condition links the computational complexity a priorily to the number...

An Optimal Adaptive Finite Element Method for the Stokes Problem

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

An Absolutely Stabilized Finite Element Method for the Stokes Problem

An absolutely stabilized finite element formulation for the Stokes problem is presented in this paper. This new formulation, which is nonsymmetric but stable without employment of any stability constant, can be regarded as a modification of the formulation proposed recently by Hughes and Franca in [8]. Optimal error estimates in L2-norm for the new stabilized finite element approximation of bot...

An Eulerian Finite Element Method for Elliptic Equations on Moving Surfaces

In this paper a new finite element approach for the discretization of elliptic partial differential equations on surfaces is treated. The main idea is to use finite element spaces that are induced by triangulations of an “outer” domain to discretize the partial differential equation on the surface. The method is particularly suitable for problems in which there is a coupling with a flow problem...