@article {Bueler:March 2005:0022-1430:291,
	author = "Bueler, Ed",
	author = "Lingle, Craig S.",
	author = "Kallen-Brown, Jed A.",
	author = "Covey, David N.",
	author = "Bowman, Latrice N.",
	title = "Exact solutions and verification of numerical models for isothermal ice sheets",
	journal = "Journal of Glaciology",
	volume = "51",
	year = "March 2005",
	abstract = "Comparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with 'compensatory accumulation'. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidal-in-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.",
	pages = "291-306(16)",
	url = "http://www.ingentaconnect.com/content/igsoc/jog/2005/00000051/00000173/art00011"
	doi = "doi:10.3189/172756505781829449"
}