Section: New Results

A high order method for the approximation of integrals over simplicity defined hypersurfaces

Participants : Lukas Drescher, Holger Heumann, Kersten Schmidt.

We introduced a novel method to compute approximations of integrals over implicitly defined hypersurfaces. The new method is based on a weak formulation in L2(0,1) that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral finite element methods, and the expensive computation of explicit hypersurface parametrizations is avoided. We derived error estimates showing that high order convergence can be achieved provided the integrand and the hypersurface defining function are sufficiently smooth.