A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm
- Univ. of New Mexico, Albuquerque, NM (United States)
- Colorado State Univ., Fort Collins, CO (United States)
- Univ. of Colorado, Denver, CO (United States)
- PD&L, DigitalGlobe, Inc., Longmont, CO (United States)
We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute “dual-weighted” a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.
- Research Organization:
- Colorado State Univ., Fort Collins, CO (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0005304; SC0009279; SC0009324; FG02-04ER25620; FG02-05ER25699; FC02-07ER54909; SC0001724
- OSTI ID:
- 1467608
- Journal Information:
- SIAM Journal on Numerical Analysis, Vol. 54, Issue 5; ISSN 0036-1429
- Publisher:
- Society for Industrial and Applied MathematicsCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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