On the accuracy of finite element approximations to a class of interface problems

Guzmán, Johnny; Sánchez, Manuel; Sarkis, Marcus

doi:10.1090/mcom3051

On the accuracy of finite element approximations to a class of interface problems
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by Johnny Guzmán, Manuel A. Sánchez and Marcus Sarkis PDF

Math. Comp. 85 (2016), 2071-2098 Request permission

Abstract:

We define piecewise linear and continuous finite element methods for a class of interface problems in two dimensions. Correction terms are added to the right-hand side of the natural method to render it second-order accurate. We prove that the method is second-order accurate on general quasi-uniform meshes at the nodal points. Finally, we show that the natural method, although non-optimal near the interface, is optimal for points $\mathcal {O}(\sqrt {h \log (\frac {1}{h})})$ away from the interface.

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