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• W2527756105 abstract "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 and 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 the formulation of the adjoint problems. We apply the analysis to computing “dual-weighted” a posteriori error estimates, developing 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." @default.
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• W2527756105 date "2016-01-01" @default.
• W2527756105 modified "2023-10-17" @default.
• W2527756105 title "A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm" @default.
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• W2527756105 doi "https://doi.org/10.1137/16m1079014" @default.
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