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Applications to Problems with Singularity

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Artificial Boundary Method

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Abstract

In this chapter, we discuss the application of ABCs for some problems with singularity, including the modified Helmholtz equation with singularity, the interface problem, the linear elastic system with singularity, and the Stokes equations with singularity. By using artificial boundaries, the singular points are removed, and the original problems are reduced to boundary value problems on computational domains. Boundary conditions on the artificial boundaries are obtained, and then the finite element method is applied to solve the reduced problems. Some error estimates are also given.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Houde Han

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Xiaonan Wu

Authors
  1. Houde Han
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  2. Xiaonan Wu
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© 2013 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg

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Han, H., Wu, X. (2013). Applications to Problems with Singularity. In: Artificial Boundary Method. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35464-9_10

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