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Volume 5, Issue 5
Convergence of High Order Methods for Miscible Displacement

Y. Epshteyn & B. Rivière

Int. J. Numer. Anal. Mod., 5 (2008), pp. 47-63.

Published online: 2018-11

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  • Abstract

We derive error estimates for fully discrete scheme using primal discontinuous Galerkin discretization in space and backward Euler discretization in time. The estimates in the energy norm are optimal with respect to the mesh size and suboptimal with respect to the polynomial degree. The proposed scheme is of high order as polynomial approximations of pressure and concentration can take any degree. In addition, the method can handle different types of boundary conditions and is well-suited for unstructured meshes.

  • Keywords

flow, transport, porous media, miscible displacement, NIPG, SIPG, IIPG, h and p-version, fully discrete scheme.

  • AMS Subject Headings

35Q35, 65N30, 65N15, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-47, author = {Epshteyn , Y. and Rivière , B.}, title = {Convergence of High Order Methods for Miscible Displacement}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {5}, number = {5}, pages = {47--63}, abstract = {

We derive error estimates for fully discrete scheme using primal discontinuous Galerkin discretization in space and backward Euler discretization in time. The estimates in the energy norm are optimal with respect to the mesh size and suboptimal with respect to the polynomial degree. The proposed scheme is of high order as polynomial approximations of pressure and concentration can take any degree. In addition, the method can handle different types of boundary conditions and is well-suited for unstructured meshes.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/839.html} }
TY - JOUR T1 - Convergence of High Order Methods for Miscible Displacement AU - Epshteyn , Y. AU - Rivière , B. JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 47 EP - 63 PY - 2018 DA - 2018/11 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/839.html KW - flow, transport, porous media, miscible displacement, NIPG, SIPG, IIPG, h and p-version, fully discrete scheme. AB -

We derive error estimates for fully discrete scheme using primal discontinuous Galerkin discretization in space and backward Euler discretization in time. The estimates in the energy norm are optimal with respect to the mesh size and suboptimal with respect to the polynomial degree. The proposed scheme is of high order as polynomial approximations of pressure and concentration can take any degree. In addition, the method can handle different types of boundary conditions and is well-suited for unstructured meshes.

Epshteyn , Y. and Rivière , B.. (2018). Convergence of High Order Methods for Miscible Displacement. International Journal of Numerical Analysis and Modeling. 5 (5). 47-63. doi:
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