A hybrid mass transport finite element method for Keller-Segel type systems

We propose a new splitting scheme for general reaction–taxis–diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well as travelling waves and merging phenomena. The splitting scheme is based on a mass transport strategy for the cell density coupled with classical finite element approximations for the rest of the system. The built-in mass adaption of the scheme allows for an excellent performance even with respect to dedicated mesh-adapted AMR schemes in original variables

A multi-scale method for complex flows of non-Newtonian fluids

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids

On the error estimate of a combined finite element - finite volume method

We present the error analysis of an efficient numerical method for solving the scalar nonliner conservation law equation with a diffusion term. The main idea of the method is to discretize nonlinear convective terms with the aid of monotone finite volume method, whereas the rest diffusion terms are discretized by the conforming piecewise linear finite element method. It is shown that the error is of the first order, i.e. O(h), which is optimal in this case. (orig.)SIGLEAvailable from TIB Hannover: RR 4487(1996,9) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Combined finite element - finite volume method (convergence analysis)

We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Duffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion equation. We prove the convergence of the numerical solution to the exact solution. (orig.)SIGLEAvailable from TIB Hannover: RR 4487(1996,11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system

SIGLEAvailable from TIB Hannover: RR 4487(2003,21) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On the boundary conditions for EG-methods applied to the two-dimensional wave equation system

SIGLEAvailable from TIB Hannover: RR 4487(2003,22) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Finite volume evolution Galerkin methods for nonlinear hyperbolic systems

SIGLEAvailable from TIB Hannover: RR 4487(2002,2) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman