Numerical Resolution Near <em>t</em>=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1
Year: 2011
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 568–586
Abstract
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical scheme in use. Applications of the remedy procedures to the 1D viscous Burgers equation, and to the 1D nonlinear reaction-diffusion equation are presented. The remedy procedures are applicable to other nonlinear diffusion equations as well.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.110909.160310s
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 568–586
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
-
Analysis of a Penalty Method
Chen, Qingshan | Hong, Youngjoon | Temam, RogerJournal of Scientific Computing, Vol. 53 (2012), Iss. 1 P.3
https://doi.org/10.1007/s10915-011-9553-8 [Citations: 3] -
Treatment of incompatible initial and boundary data for parabolic equations in higher dimension
Chen, Qingshan | Qin, Zhen | Temam, RogerMathematics of Computation, Vol. 80 (2011), Iss. 276 P.2071
https://doi.org/10.1090/S0025-5718-2011-02469-5 [Citations: 13] -
Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners
Gie, Gung-Min | Jung, Chang-Yeol | Temam, RogerInternational Journal of Differential Equations, Vol. 2013 (2013), Iss. P.1
https://doi.org/10.1155/2013/532987 [Citations: 2] -
Penalty method for the KdV equation
Qin, Zhen | Temam, RogerApplicable Analysis, Vol. 91 (2012), Iss. 2 P.193
https://doi.org/10.1080/00036811.2011.579564 [Citations: 1] -
On the Prandtl Boundary Layer Equations in Presence of Corner Singularities
Cannone, M. | Lombardo, M. C. | Sammartino, M.Acta Applicandae Mathematicae, Vol. 132 (2014), Iss. 1 P.139
https://doi.org/10.1007/s10440-014-9912-1 [Citations: 9] -
Recent progresses in boundary layer theory
Temam, Roger | Jung, Chang-Yeol | Gie, Gung-MinDiscrete and Continuous Dynamical Systems, Vol. 36 (2015), Iss. 5 P.2521
https://doi.org/10.3934/dcds.2016.36.2521 [Citations: 9] -
Navier–Stokes Equations in the Half Space with Non Compatible Data
Argenziano, Andrea | Cannone, Marco | Sammartino, MarcoJournal of Mathematical Fluid Mechanics, Vol. 26 (2024), Iss. 2
https://doi.org/10.1007/s00021-024-00863-6 [Citations: 1] -
Well-posedness of Prandtl equations with non-compatible data
Cannone, M | Lombardo, M C | Sammartino, MNonlinearity, Vol. 26 (2013), Iss. 12 P.3077
https://doi.org/10.1088/0951-7715/26/12/3077 [Citations: 28] -
A penalty method for numerically handling dispersive equations with incompatible initial and boundary data
Flyer, Natasha | Qin, Zhen | Temam, RogerNumerical Methods for Partial Differential Equations, Vol. 28 (2012), Iss. 6 P.1996
https://doi.org/10.1002/num.21693 [Citations: 1] -
Asymptotic analysis of the Navier-Stokes equations in a curved domain with a non-characteristic boundary
Gie, Gung-Min | Hamouda, Makram | Temam, RogerNetworks & Heterogeneous Media, Vol. 7 (2012), Iss. 4 P.741
https://doi.org/10.3934/nhm.2012.7.741 [Citations: 13]