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HP-Adaptive Time-Discontinuous Galerkin Finite Element Methods for Time-Dependent Waves

[+] Author Affiliations
Sethuramalingam Subbarayalu, Lonny L. Thompson

Clemson University

Paper No. IMECE2004-60403, pp. 245-256; 12 pages
  • ASME 2004 International Mechanical Engineering Congress and Exposition
  • Noise Control and Acoustics
  • Anaheim, California, USA, November 13 – 19, 2004
  • Conference Sponsors: Noise Control and Acoustics Division
  • ISBN: 0-7918-4715-2 | eISBN: 0-7918-4178-2, 0-7918-4179-0, 0-7918-4180-4
  • Copyright © 2004 by ASME


hp-Adaptive time-discontinuous Galerkin methods are developed for second-order hyperbolic systems. Explicit a priori error estimates in terms of time-step size, approximation order, and solution regularity are derived. Knowledge of these a priori convergence rates in combination with a posteriori error estimates computed from the jump in time-discontinuous solutions are used to automatically select time-step size h and approximation order p to achieve a specified error tolerance with a minimal number of total degrees-of-freedom. We show that the temporal jump error is a good indicator of the local error, and the summation of jump error for the total interval is good indicator for the global and accumulation errors. In addition, the accumulation error at the end of a time-step can be estimated well by the summation of the local jump error at the beginning of a time-step provided the approximation order is greater or equal to the solution regularity. Superconvergence of the end points of a time-step for high-order polynomials are also demonstrated.

Copyright © 2004 by ASME



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