We discuss a new approach to finite element methods for partial differential equations (PDEs) over non-polyhedral domains. We transform PDEs from a physical domain to analogous PDEs over a parametric domain.
The transformed PDE generally involves smooth coefficients, whose approximation leads to a variational crime in the finite element method. Only recent results in approximation confirm optimal error estimates. We also point out some gaps in the literature. We present examples from computational physics.
Tuesday, January 30, 2018
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813