Peter Giesl

Learn More
In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collo-cation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless colloca-tion to approximate Lyapunov functions for dynamical(More)
— The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to compute a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to(More)
— An integral part of the CPA method to compute Continuous and Piecewise Affine Lyapunov functions for nonlinear systems is the generation of a suitable triangulation. Recently, the CPA method was revised by using more advanced triangulations and it was proved that it can compute a CPA Lya-punov function for any nonlinear system possessing an exponentially(More)
We present a model of the human elbow and study the problem of existence and stability of equilibrium states. Our main goal is to demonstrate that stable equilibrium states exist just on grounds of the mechanical properties of the muscles and the skeleton. In particular, additional control mechanisms such as reflexes are not necessary to obtain stability.(More)
  • 1