Arbitrage-free prices u of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) ∂tu +A[u] = 0. This… (More)

A new nite element method for elliptic problems with locally periodic microstructure of length " > 0 is developed and analyzed. It is shown that the method converges, as " ! 0, to the solution of the… (More)

We numerically solve parabolic problems in , , where is a bounded interval and is a strongly elliptic integrodifferential operator of order ! #" %$'& . A discontinuous Galerkin (dG) discretization in… (More)

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε 1. Based on a refined two-scale… (More)

The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test… (More)

In this paper we analyze the performance of the hp?Finite Element Method for a cylindrical shell problem. Our theoretical investigations show that the hp approximation converges exponentially,… (More)

The numerical solution of parabolic problems ut + Au = 0 with a pseudodifferential operator A by wavelet discretization in space and hp discontinuous Galerkin time stepping is analyzed. It is proved… (More)