Volume 2, Issue 2
Green's Function Estimates for a Singularly Perturbed Convection-Diffusion Problem in Three Dimensi

Sebastian Franz & Natalia Kopteva

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 124-141

Published online: 2011-02

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  • Abstract
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its firstand second-order derivatives are established in the L_1 norm by employing the parametrix metho'. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem to derive a robust a posteriori error estimator in the maximum norm.
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@Article{IJNAMB-2-124, author = {Sebastian Franz and Natalia Kopteva}, title = { Green's Function Estimates for a Singularly Perturbed Convection-Diffusion Problem in Three Dimensi}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {2}, pages = {124--141}, abstract = {A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its firstand second-order derivatives are established in the L_1 norm by employing the parametrix metho'. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem to derive a robust a posteriori error estimator in the maximum norm.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/303.html} }
TY - JOUR T1 - Green's Function Estimates for a Singularly Perturbed Convection-Diffusion Problem in Three Dimensi AU - Sebastian Franz & Natalia Kopteva JO - International Journal of Numerical Analysis Modeling Series B VL - 2 SP - 124 EP - 141 PY - 2011 DA - 2011/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/303.html KW - AB - A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its firstand second-order derivatives are established in the L_1 norm by employing the parametrix metho'. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem to derive a robust a posteriori error estimator in the maximum norm.
Sebastian Franz and Natalia Kopteva. (2011). Green's Function Estimates for a Singularly Perturbed Convection-Diffusion Problem in Three Dimensi. International Journal of Numerical Analysis Modeling Series B. 2 (2). 124-141. doi:
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