Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary
J. Karátson, B. Kovács, S. Korotov, IMA Journal of Numerical Analysis 40 (2018) 1241–1265.
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Journal Article
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| English
Author
Karátson, János;
Kovács, BalázsLibreCat 
;
Korotov, Sergey
;
Korotov, SergeyDepartment
Abstract
<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci & Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>
Publishing Year
Journal Title
IMA Journal of Numerical Analysis
Volume
40
Issue
2
Page
1241-1265
LibreCat-ID
Cite this
Karátson J, Kovács B, Korotov S. Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. IMA Journal of Numerical Analysis. 2018;40(2):1241-1265. doi:10.1093/imanum/dry086
Karátson, J., Kovács, B., & Korotov, S. (2018). Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary. IMA Journal of Numerical Analysis, 40(2), 1241–1265. https://doi.org/10.1093/imanum/dry086
@article{Karátson_Kovács_Korotov_2018, title={Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}, volume={40}, DOI={10.1093/imanum/dry086}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Karátson, János and Kovács, Balázs and Korotov, Sergey}, year={2018}, pages={1241–1265} }
Karátson, János, Balázs Kovács, and Sergey Korotov. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” IMA Journal of Numerical Analysis 40, no. 2 (2018): 1241–65. https://doi.org/10.1093/imanum/dry086.
J. Karátson, B. Kovács, and S. Korotov, “Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary,” IMA Journal of Numerical Analysis, vol. 40, no. 2, pp. 1241–1265, 2018, doi: 10.1093/imanum/dry086.
Karátson, János, et al. “Discrete Maximum Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.” IMA Journal of Numerical Analysis, vol. 40, no. 2, Oxford University Press (OUP), 2018, pp. 1241–65, doi:10.1093/imanum/dry086.
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