Accurate gradient computations at interfaces using finite element methods - Qin, Fangfang; Wang, Zhaohui; Ma, Zhijie; Li, Zhilin (Zielona Góra: Uniwersytet Zielonogórski)
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of Wheeler (1974). For 2D interface problems, the point is to introduce a small tube near the interface and propose the gradient as part of unknowns, which is similar to a mixed finite element method, but only at the interface. Thus the computational cost is just slightly higher than in the standard finite element method.
Keywords: elliptic interface problems; gradient/flux computation; IFEM; mixed FE formulation; computational tube