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Paper details
Number 3 - September 2017
Volume 27 - 2017
Accurate gradient computations at interfaces using finite element methods
Fangfang Qin, Zhaohui Wang, Zhijie Ma, Zhilin Li
Abstract
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. We present a
rigorous one dimensional analysis, which shows a second order convergence order for both the solution and the gradient in
1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution,
and super-convergence for the gradient at the interface.
Keywords
elliptic interface problems, gradient/flux computation, IFEM, mixed FE formulation, computational tube