Paper Info
Title
Verification of reduced convergence rates
Abstract
In this short article, we recalculate the numerical example in Krízek and Neittaanmäki (1987) for the Poisson solution u - xσ(1-x) sin πy in the unit square S as σ = 7/4. By the finite difference method, an error analysis for such a problem is given from our previous study by ||ε||1 = C1h2 - C2h5/4, where h is the meshspacing of the uniform square grids used, and C1 and C2 are two positive constants. Let ε = u - uh, where uh is the finite difference solution, and ||ε||2 is the discrete H1 norm. Several techniques are employed to confirm the reduced rate O(h5/4) of convergence, and to give the constants. C1 = 0.09034 and C2 = 0.002275 for a stripe domain. The better performance for σ = 7/4 arises from the fact that the constant C1 is much large than C2, and the h in computation is not small enough.
Year
DOI
Venue
2005
10.1007s00607-004-0079-x
Computing
Keywords
DocType
Volume
numerical verification,reduced convergence rates,superconvergence,singularity,poisson equation.
Journal
74
Issue
ISSN
Citations 
1
1436-5057
1
PageRank 
References 
Authors
0.69
0
2
Name
Order
Citations
PageRank
Hsin-Yun Hu121.43
Zi-Cai Li212518.79