Volume 7, Issue 3
The Two-level Local Projection Stablization as an Enriched One-level Approach, a One-dimensional Study

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 onelevel 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 guarentee that the linear part of the solution becomes nodally exact.
• Keywords

Local projection stabilization finite elements Shishkin mesh convection diffusion equation

65N12 65L10 65N30

@Article{IJNAM-7-520, author = {L. Tobiska and C. Winkel}, title = {The Two-level Local Projection Stablization 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 onelevel 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 guarentee 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 Stablization 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 KW - finite elements KW - Shishkin mesh KW - convection diffusion equation AB - The two-level local projection stabilization is considered as a onelevel 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 guarentee that the linear part of the solution becomes nodally exact.