Elliptic Poincaré-Steklov Operators
Solution of the elliptic equations with heterogeneous coefficients by reduction to the interface is based on a separation of the physical domain into subregions which can be modelled with smooth and nearly constant (homogeneous) coefficients. The union of interfaces between subdomains (also called the skeleton) is handled by continuity conditions for the Cauchy data associated with the given elliptic operator (for example, velocities and fluxes in fluid dynamics, and stress and strain tensors in structural mechanics). The corresponding interface equations govern the weak continuity of traces (Dirichlet continuity) and conormal derivatives (Neumann continuity) according to the geometrical domain decomposition. In particular, in absence of external inputs this principle leads to the conservation of fluxes in the fluid dynamics. In this way, the reduction of elliptic PDEs to the interface has a deep physical background.
KeywordsBoundary Element Method Solution Operator Trace Theorem Trace Space Boundary Integral Operator
Unable to display preview. Download preview PDF.