## 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.## References

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## Additional Information

**Johnny Guzmán**- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
- MR Author ID: 775211
- Email: johnny_guzman@brown.edu
**Manuel A. Sánchez**- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
- MR Author ID: 895873
- Email: manuel_sanchez_uribe@brown.edu
**Marcus Sarkis**- Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609
- MR Author ID: 358674
- Email: msarkis@wpi.edu
- Received by editor(s): March 28, 2014
- Received by editor(s) in revised form: October 10, 2014, December 31, 2014, and February 25, 2015
- Published electronically: November 10, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp.
**85**(2016), 2071-2098 - MSC (2010): Primary 65N30, 65N15
- DOI: https://doi.org/10.1090/mcom3051
- MathSciNet review: 3511275