A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems. Chaudhry, J., Estep, D., Ginting, V., & Tavener, S. SIAM/ASA Journal on Uncertainty Quantification, 3(1):434-459, 2015.
Paper doi abstract bibtex We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem.
@article {MR3354999,
AUTHOR = {Chaudhry, J. and Estep, D. and Ginting, V. and Tavener, S.},
TITLE = {A {P}osteriori {A}nalysis for {I}terative {S}olvers for {N}onautonomous
{E}volution {P}roblems},
JOURNAL = {SIAM/ASA Journal on Uncertainty Quantification},
VOLUME = {3},
YEAR = {2015},
NUMBER = {1},
PAGES = {434-459},
ISSN = {2166-2525},
MRCLASS = {65L05 (65L07 65L20 65L70)},
MRNUMBER = {3354999},
DOI = {10.1137/130949403},
URL = {http://dx.doi.org/10.1137/130949403},
ABSTRACT="We derive, implement, and test a posteriori error estimates for numerical methods for a nonautonomous linear system that involve iterative solution of the discrete equations. We consider two iterations: the Picard iteration and the Jacobi iteration for solving the discrete matrix-vector equations. To carry out the analysis, we define an appropriate adjoint problem for the numerical approximations using the matricant. We present a number of examples with interesting characteristics to illustrate the effectiveness of the estimate. We also present a comparison between the a posteriori error estimate and a conceptually simpler estimate obtained with a 'pseudoadjoint' problem."
}
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