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Volume 7, Issue 3
The Two-Level Local Projection Stabilization as an Enriched One-Level Approach. A One-Dimensional Study

L. Tobiska & C. Winkel

Int. J. Numer. Anal. Mod., 7 (2010), pp. 520-534.

Published online: 2010-07

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  • Abstract

The two-level local projection stabilization is considered as a one-level approach in which the enrichments on each element are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the convergence order. For example, using continuous piecewise polynomials of degree $r \geq 1$, only one function per cell is needed as enrichment instead of $r$ in the two-level approach. Moreover, in the constant coefficient case, we derive formulas for the user-chosen stabilization parameter which guarantee that the linear part of the solution becomes nodally exact.

  • Keywords

Local projection stabilization, finite elements, Shishkin mesh, convection diffusion equation.

  • AMS Subject Headings

65N12, 65L10, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-520, author = {L. Tobiska and C. Winkel}, title = {The Two-Level Local Projection Stabilization as an Enriched One-Level Approach. A One-Dimensional Study}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {520--534}, abstract = {

The two-level local projection stabilization is considered as a one-level approach in which the enrichments on each element are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the convergence order. For example, using continuous piecewise polynomials of degree $r \geq 1$, only one function per cell is needed as enrichment instead of $r$ in the two-level approach. Moreover, in the constant coefficient case, we derive formulas for the user-chosen stabilization parameter which guarantee that the linear part of the solution becomes nodally exact.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/735.html} }
TY - JOUR T1 - The Two-Level Local Projection Stabilization as an Enriched One-Level Approach. A One-Dimensional Study AU - L. Tobiska & C. Winkel JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 520 EP - 534 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/735.html KW - Local projection stabilization, finite elements, Shishkin mesh, convection diffusion equation. AB -

The two-level local projection stabilization is considered as a one-level approach in which the enrichments on each element are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the convergence order. For example, using continuous piecewise polynomials of degree $r \geq 1$, only one function per cell is needed as enrichment instead of $r$ in the two-level approach. Moreover, in the constant coefficient case, we derive formulas for the user-chosen stabilization parameter which guarantee that the linear part of the solution becomes nodally exact.

L. Tobiska and C. Winkel. (2010). The Two-Level Local Projection Stabilization as an Enriched One-Level Approach. A One-Dimensional Study. International Journal of Numerical Analysis and Modeling. 7 (3). 520-534. doi:
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