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Volume 14, Issue 1
Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements

S.-H. Chou & C. Attanayake

Int. J. Numer. Anal. Mod., 14 (2017), pp. 88-102.

Published online: 2016-01

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  • Abstract

We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method introduced by Lin et al. in [13]. The recovery is done at nodes and interface point first and by interpolation at the remaining points. In the case of piecewise constant diffusion coefficient, we show that the end nodes are superconvergence points for both the primary variable $p$ and its flux $u$. Furthermore, in the case of piecewise constant diffusion coefficient without the absorption term the errors at end nodes and interface point in the approximation of $u$ and $p$ are zero. In the general case, flux error at end nodes and interface point is third order. Numerical results are provided to confirm the theory.

  • Keywords

Recovery technique, quadratic immersed interface method, Superconvergence, conservative method, Green's function.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-88, author = {}, title = {Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {14}, number = {1}, pages = {88--102}, abstract = {

We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method introduced by Lin et al. in [13]. The recovery is done at nodes and interface point first and by interpolation at the remaining points. In the case of piecewise constant diffusion coefficient, we show that the end nodes are superconvergence points for both the primary variable $p$ and its flux $u$. Furthermore, in the case of piecewise constant diffusion coefficient without the absorption term the errors at end nodes and interface point in the approximation of $u$ and $p$ are zero. In the general case, flux error at end nodes and interface point is third order. Numerical results are provided to confirm the theory.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/412.html} }
TY - JOUR T1 - Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 88 EP - 102 PY - 2016 DA - 2016/01 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/412.html KW - Recovery technique, quadratic immersed interface method, Superconvergence, conservative method, Green's function. AB -

We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method introduced by Lin et al. in [13]. The recovery is done at nodes and interface point first and by interpolation at the remaining points. In the case of piecewise constant diffusion coefficient, we show that the end nodes are superconvergence points for both the primary variable $p$ and its flux $u$. Furthermore, in the case of piecewise constant diffusion coefficient without the absorption term the errors at end nodes and interface point in the approximation of $u$ and $p$ are zero. In the general case, flux error at end nodes and interface point is third order. Numerical results are provided to confirm the theory.

S.-H. Chou & C. Attanayake. (1970). Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements. International Journal of Numerical Analysis and Modeling. 14 (1). 88-102. doi:
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