Abstract
In this short article, we recalculate the numerical example in Krizek and Neittaanmaki (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 ||e||1 = C1h2 - C2h5/4, where h is the meshspacing of the uniform square grids used, and C1 and C2 are two positive constants. Let e = u - uh, where uh is the finite difference solution, and ||e||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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
