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A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods

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Abstract

In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic second-order elliptic interface problem. The error estimation shows that these methods can converge optimally in a mesh-dependent energy norm. The combination of IFEs and DG formulation in these methods allows local mesh refinement in the Cartesian mesh structure for interface problems. Numerical results are provided to demonstrate the convergence and local mesh refinement features of these DG-IFE methods.

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Acknowledgments

The authors would like to thank anonymous referees whose comments and suggestions enhanced the presentation of our research work.

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Correspondence to Xu Zhang.

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This work is partially supported by NSF grant DMS-1016313.

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Lin, T., Yang, Q. & Zhang, X. A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods. J Sci Comput 65, 875–894 (2015). https://doi.org/10.1007/s10915-015-9989-3

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  • DOI: https://doi.org/10.1007/s10915-015-9989-3

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