An element-local L2-projected C0 finite element method is presented to approximate the nonsmooth solution being not in H1 of the Maxwell problem on a nonconvex Lipschitz polyhedron with reentrant corners and edges. The key idea lies in that element-local L2 projectors are applied to both curl and div operators. The C0 linear finite element (enriched with certain higher degree bubble functions) is employed to approximate the nonsmooth solution. The coercivity in L2 norm is established uniform in the mesh-size, and the condition number O(h-2) of the resulting linear system is proven. For the solution and its curl in Hr with r < 1 we obtain an error bound O(hr) in an energy norm. Numerical experiments confirm the theoretical error bound.
- Maxwell problem
- Nonsmooth solution
- C0 finite element method
- L2 projection
Duan, H-Y., Jia, F., Lin, P., & Tan, R. C. E. (2009). The Local $L^2$ Projected $C^0$ Finite Element Method for Maxwell Problem. SIAM Journal on Numerical Analysis, 47(2), 1274-1303. https://doi.org/10.1137/070707749