New England Numerical Analysis Day 2009

University of Rhode Island
Department of Mathematics, Lippitt Hall
April 4, 2009, 9:00am-5:30pm
main conference page

Changes in the Solution from Curved Domain to Polygon

Gilbert Strang, MIT

The area between a unit circle and an inscribed n-sided regular polygon is not hard to compute. What is important is that this gives the leading term in the difference in the eigenvalues for polygons and circles -- if they were "drums" and we solve Laplace's eigenvalue problem to find the natural vibration frequencies.

This leads to a practical suggestion for the eigenvalue problem (and for other problems too): Let the polygon go outside the circle enough to have the same area. Then the error from changing to a polygon and creating a mesh and solving by finite elements is much reduced. The next term in the error is found and it involves the Riemann zeta function...



Organizers

Jim Baglama (URI), Tom Bella (URI), Li Wu (URI).

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