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Volume 8, Issue 1
Robust a-Posteriori Estimators for Multilevel Discretizations of Reaction-Diffusion Systems

V. Klein & M. Peszynska

Int. J. Numer. Anal. Mod., 8 (2011), pp. 1-27.

Published online: 2011-08

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  • Abstract

We define a multilevel finite element discretization for a coupled stationary reaction-diffusion system in which each component can be defined on a separate grid. We prove convergence of the scheme and propose residual a-posteriori estimators for the error in the natural energy norm for the system. The estimators are robust in the coefficients of the system. We prove upper and lower bounds and illustrate the theory with numerical experiments.

  • Keywords

multilevel finite elements, a-priori error estimates, a-posteriori error estimators, reaction-diffusion system.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-1, author = {V. Klein and M. Peszynska}, title = {Robust a-Posteriori Estimators for Multilevel Discretizations of Reaction-Diffusion Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {1}, pages = {1--27}, abstract = {

We define a multilevel finite element discretization for a coupled stationary reaction-diffusion system in which each component can be defined on a separate grid. We prove convergence of the scheme and propose residual a-posteriori estimators for the error in the natural energy norm for the system. The estimators are robust in the coefficients of the system. We prove upper and lower bounds and illustrate the theory with numerical experiments.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/671.html} }
TY - JOUR T1 - Robust a-Posteriori Estimators for Multilevel Discretizations of Reaction-Diffusion Systems AU - V. Klein & M. Peszynska JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 27 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/671.html KW - multilevel finite elements, a-priori error estimates, a-posteriori error estimators, reaction-diffusion system. AB -

We define a multilevel finite element discretization for a coupled stationary reaction-diffusion system in which each component can be defined on a separate grid. We prove convergence of the scheme and propose residual a-posteriori estimators for the error in the natural energy norm for the system. The estimators are robust in the coefficients of the system. We prove upper and lower bounds and illustrate the theory with numerical experiments.

V. Klein and M. Peszynska. (2011). Robust a-Posteriori Estimators for Multilevel Discretizations of Reaction-Diffusion Systems. International Journal of Numerical Analysis and Modeling. 8 (1). 1-27. doi:
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