SIAM Journal on Numerical Analysis · 2002 · 745 citations · 13 references
ComputingComputational EngineeringPhysicsComputational Fluid DynamicsComputational MechanicsFluid DynamicsConvergence AnalysisError EstimationNumerical ConvergenceTime IntegrationTime Integration SchemesDiscretizationGalerkin DiscretizationNonlinear SystemsProper Orthogonal DecompositionTime DiscretizationTime Discretization Error Analysis
Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear parabolic systems arising in fluid dynamics are proved. For the time integration the backward Euler scheme is considered. The asymptotic estimates involve the singular values of the POD snapshot set and the grid-structure of the time discretization as well as the snapshot locations.
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