Abstract
In this paper we present a novel design of a unified variational framework for both time continuous and discontinuous integration operators and also discuss in particular their equivalence via their respective spectral properties. As an added dimension, we also describe how the proposed approach enables the design of both time continuous/discontinuous high-order A-Stable schemes of order 2q, L-Stable schemes of order 2q - 1 and 2q - 2, and subsequently provide the requisite hierarchical computational structure of the resulting equations that is useful for time adaptive computations. In this regard, a new unified set of energy conserving and energy dissipating time discretized operators are described for both time continuous and discontinuous formulations for computational dynamics. Although the emphasis is placed on second-order systems, the developments also hold for first-order system representations.
Original language | English (US) |
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Pages (from-to) | 727-749 |
Number of pages | 23 |
Journal | Finite elements in analysis and design |
Volume | 39 |
Issue number | 8 |
DOIs | |
State | Published - May 2003 |
Bibliographical note
Funding Information:The authors are very pleased to acknowledge support in part by Battelle/US Army Research Office (ARO) Research Triangle Park, North Carolina, under Grant no. DAAH04-96-C-0086, and by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory (ARL) under contact no. DAAD19-01-2-0014. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Support in part by Dr. Raju Namburu and Dr. Andrew Mark is also gratefully acknowledged. Special thanks are due to the CIS Directorate at the US Army Research Laboratory (ARL), Aberdeen Proving Ground, Maryland. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota is also gratefully acknowledged.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
Keywords
- Bi-discontinuous formulations
- Continuous and discontinuous Galerkin and Petrov-Galerkin methods
- Continuous/discontinuous time operators
- High-order time integration operators
- Weighted residual method