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Volume 11, Issue 4
Analysis of the Discontinuous Galerkin Interior Penalty Method with Solenoidal Approximations for the Stokes Equations

A. Montlaur & S. Fernandez-Mendez

Int. J. Numer. Anal. Mod., 11 (2014), pp. 715-725.

Published online: 2014-11

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  • Abstract

The discontinuous Galerkin Interior Penalty Method with solenoidal approximations proposed in [13] for the incompressible Stokes equations is analyzed. Continuity and coercivity of the bilinear form are proved. A priori error estimates, with optimal convergence rates, are derived. 2D and 3D numerical examples with known analytical solution corroborate the theoretical analysis.

  • Keywords

Discontinuous Galerkin, Stokes equations, incompressible flow, divergence-free, Interior Penalty Method, error bounds.

  • AMS Subject Headings

35Q35, 65G99, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-715, author = {A. Montlaur and S. Fernandez-Mendez}, title = {Analysis of the Discontinuous Galerkin Interior Penalty Method with Solenoidal Approximations for the Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {715--725}, abstract = {

The discontinuous Galerkin Interior Penalty Method with solenoidal approximations proposed in [13] for the incompressible Stokes equations is analyzed. Continuity and coercivity of the bilinear form are proved. A priori error estimates, with optimal convergence rates, are derived. 2D and 3D numerical examples with known analytical solution corroborate the theoretical analysis.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/548.html} }
TY - JOUR T1 - Analysis of the Discontinuous Galerkin Interior Penalty Method with Solenoidal Approximations for the Stokes Equations AU - A. Montlaur & S. Fernandez-Mendez JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 715 EP - 725 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/548.html KW - Discontinuous Galerkin, Stokes equations, incompressible flow, divergence-free, Interior Penalty Method, error bounds. AB -

The discontinuous Galerkin Interior Penalty Method with solenoidal approximations proposed in [13] for the incompressible Stokes equations is analyzed. Continuity and coercivity of the bilinear form are proved. A priori error estimates, with optimal convergence rates, are derived. 2D and 3D numerical examples with known analytical solution corroborate the theoretical analysis.

A. Montlaur and S. Fernandez-Mendez. (2014). Analysis of the Discontinuous Galerkin Interior Penalty Method with Solenoidal Approximations for the Stokes Equations. International Journal of Numerical Analysis and Modeling. 11 (4). 715-725. doi:
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