演講訊息 TALKS

We talk about a new C0 finite element method for Maxwell’s equations. Such equations are formulated in terms of curl and div operators. The well-known challenging task for this type of problem is how to use C0 Lagrange elements to numerically solve the singular solution that may be not in H1. The classical C0 finite element method fails to produce a correct convergent solution; meanwhile, even adaptive mesh-refinement technique is useless. Our new C0 finite element method can correctly capture the singular solution and gives an error bound (optimal with respect to the regularity of the exact solution). Our method can deal with any singular solution which may have the regularity from L2 to Hr for any r>0. A numerical test for Maxwell eigenproblem is presented to demonstrate the theoretical error bounds. We also address several other discretization methods, such as edge element method, singular function method, weighted method, H-1 method, discontinuous Galerkin method, finite volume/finite integration/mimetic difference method.