07/12/2000, 17:00 — 18:00 — Amphitheatre Va5, Civil Engineering Building
Wolfgang Wendland, Universität Stuttgart
Foundation and Application of Boundary Element Methods
First we consider some basic properties of integral operators as pseudodifferential operators. Boundary integral operators and non-local operators are mostly classical pseudodifferential operators defined either by the fundamental solution or a parametrix or Levi functions. The decisive properties of these operators are characterized by corresponding pseudo-homogeneous expansions of the kernels of corresponding general integral operators. These expansions are decisive for the mapping and smoothness properties of these non-local operators which one needs for appropriate discretizations. For stability and convergence of discrete schemes, strong ellipticity plays an essential role. For strongly elliptic boundary value problems, integral operators of the first kind inherit strong ellipticity under mild additional assumptions.
The lecture is based on: George C. Hsiao, Wolfgang L. Wendland: Boundary Integral Equations (in preparation).
