Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds

By Karen Veroy, Christophe Prud'Homme, Anthony T. Patera. 2003

127 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/78b4256f55067f5cfdcc572069a2d77d04ece8b3

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In Computational Mechanics

In Mechanics of Materials

In Numerical Analysis

Citations in the corpus

REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS (2011, background): “…established reduced basis approximations and associated rigorous a posteriori error bounds for nonsingular solution branches of the steady Burgers [55] and steady incompressible Navier-Stokes and Boussinesq equations [9,14,45,54]; we focus here on the unsteady case. standard Galerkin treatment. b…”
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, background): “2Note there are examples of rigorous RB a posteriori error bounds for the steady viscous Burgers equation in Veroy et al. (2003a) and the steady incompressible Navier‐Stokes equations in Deparis (2008); Nguyen et al. (2005); Veroy and Patera (2005) .”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, unknown): “There are examples of rigorous reduced basis a posteriori error bounds for the steady Burgers’ [37] and incompressible Navier-Stokes [28, 36] equations; the new contribution of the current paper is treatment of the unsteady—parabolic—case.”
Certified reduced basis approximation for parametrized partial differential equations and applications (2011, background): “Classical problems arising in applied sciences are, for example, Navier-Stokes/Boussinesq and Burgers’ equations in fluid mechanics [16, 18, 59, 17, 60, 47, 48] and nonlinear elasticity in solid mechanics.”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “3 Offline Complexity To generate the reduced basis, we use a Greedy algorithm as it is well known in the RB context [97, 73].”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, methodology): “Third, F(μ− μ̄; μ̄) is “tangent”∗ to β(μ) at μ= μ̄ – the cruder estimate (μ; μ̄) is a second-order correction: this controls the growth of J (for example, relative to simpler continuity bounds [17]).”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, methodology): “In the more recent past the reduced-basis approach and in particular associated a posteriori error estimation procedures have been successfully developed for (non)linear and (non)coercive elliptic PDEs with affine parameter dependence [23, 34, 41, 42, 43]; in this”