Abstract
Designing numerical methods with high-order accuracy for problems in irregular domains and/or with interfaces is crucial for the accurate solution of many problems with physical and biological applications. The major challenge here is to design an efficient and accurate numerical method that can capture certain properties of analytical solutions in different domains/subdomains while handling arbitrary geometries and complex structures of the domains. Moreover, in general, any standard method (finite-difference, finite-element, etc.) will fail to produce accurate solutions to interface problems due to discontinuities in the model’s parameters/solutions. In this work, we consider Difference Potentials Method (DPM) as an efficient and accurate solver for the variable coefficient elliptic interface problems.
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Acknowledgements
We are grateful to Jason Albright and Kyle R. Steffen for the comments that helped to improve the manuscript. The research of Yekaterina Epshteyn and Michael Medvinsky is supported in part by the National Science Foundation Grant # DMS-1112984.
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Epshteyn, Y., Medvinsky, M. (2015). On the Solution of the Elliptic Interface Problems by Difference Potentials Method. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_16
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DOI: https://doi.org/10.1007/978-3-319-19800-2_16
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