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Volume 47, Issue 1
A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem

Weiwei Wang & Chuanju Xu

DOI: 10.4208/jms.v47n1.14.05

J. Math. Study, 47 (2014), pp. 85-110.

Published online: 2014-03

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  • Abstract

In this paper, we carry out an a posteriori error analysis of Legendre spectral approximations to the Stokes/Darcy coupled equations. The spectral approximations are based on a weak formulation of the coupled equations by using the Beavers-Joseph-Saffman interface condition. The main contribution of the paper consists of deriving a number of posteriori error indicators and their upper and lower bounds for the single domain case. An extension of the upper bounds to the multi-domain case in the spectral element framework is also given.

  • Keywords

A posteriori error, Stokes/Darcy coupled equations, Spectral method, Spectral element method.

  • AMS Subject Headings

35Q35, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cjxu@xmu.edu.cn (Chuanju Xu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-47-85, author = {Wang , Weiwei and Xu , Chuanju}, title = {A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {1}, pages = {85--110}, abstract = {

In this paper, we carry out an a posteriori error analysis of Legendre spectral approximations to the Stokes/Darcy coupled equations. The spectral approximations are based on a weak formulation of the coupled equations by using the Beavers-Joseph-Saffman interface condition. The main contribution of the paper consists of deriving a number of posteriori error indicators and their upper and lower bounds for the single domain case. An extension of the upper bounds to the multi-domain case in the spectral element framework is also given.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n1.14.05}, url = {http://global-sci.org/intro/article_detail/jms/10113.html} }
TY - JOUR T1 - A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem AU - Wang , Weiwei AU - Xu , Chuanju JO - Journal of Mathematical Study VL - 1 SP - 85 EP - 110 PY - 2014 DA - 2014/03 SN - 47 DO - http://doi.org/10.4208/jms.v47n1.14.05 UR - https://global-sci.org/intro/article_detail/jms/10113.html KW - A posteriori error, Stokes/Darcy coupled equations, Spectral method, Spectral element method. AB -

In this paper, we carry out an a posteriori error analysis of Legendre spectral approximations to the Stokes/Darcy coupled equations. The spectral approximations are based on a weak formulation of the coupled equations by using the Beavers-Joseph-Saffman interface condition. The main contribution of the paper consists of deriving a number of posteriori error indicators and their upper and lower bounds for the single domain case. An extension of the upper bounds to the multi-domain case in the spectral element framework is also given.

Weiwei Wang & Chuanju Xu. (2019). A Posteriori Error Estimation of Spectral and Spectral Element Methods for the Stokes/Darcy Coupled Problem. Journal of Mathematical Study. 47 (1). 85-110. doi:10.4208/jms.v47n1.14.05
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