[Amath-seminars] Talk by Benjamin Seibold on March 13

Randall J LeVeque rjl at uw.edu
Tue Mar 7 22:06:40 PST 2017


Prof. Benjamin Seibold from Temple University will be visiting for a few
days next week. He will be giving a talk at 11:30 on Tuesday March 14, on
some recent interesting work on numerical methods for differential
equations...

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Speaker: Benjamin Seibold, Temple University

Title: Order Reduction in Runge-Kutta Time-Stepping for
Initial Boundary Value Problems

Time and Date: 11:30am - 12:30pm on Tuesday March 14, 2017

Place: Lewis 208 (Wan Conference Room)

Abstract:

When advancing a time-dependent PDE forward via Runge-Kutta methods, the
numerical solution may exhibit a convergence order that is less than the
actual order of the scheme. We demonstrate that this order reduction
phenomenon is in fact the norm, rather than the exception; in fact, it can
be observed in very simple problems. Geometrically, order reduction stems
from boundary layers, paradoxically caused by the fact that stage values
are too accurate near the boundary. A modal analysis reveals under which
circumstances boundary layers persist globally in time. We then present two
remedies to order reduction: (a) a property of Runge-Kutta schemes, called
weak stage order, which is compatible with DIRK schemes; and (b) modified
boundary conditions.

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