Reduced basis methods for Stokes equations in domains with non-affine parameter dependence

By Gianluigi Rozza. 2009

69 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f04381a808a789d52e8a3a1937f7dd8d365413b

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In Computational Mechanics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Certified reduced basis approximation for parametrized partial differential equations and applications (2011, background): “An interesting case of noncoercive problems is given by Stokes problems where approximation stability is guaranteed by the fullfillment of an equivalent inf-sup stability condition on the pressure term with RB approximation spaces properly enriched [41, 42].”
Parameter multi‐domain ‘hp’ empirical interpolation (2012, methodology): “In this context, the (hp-EIM or) EIM accommodates efficient offline–online computational procedures through affine approximations of the non-affine differential operator [1, 2, 4, 6, 10, 11].”
High-performance model reduction techniques in computational multiscale homogenization (2014, background): “V (in the parlance of model reduction [46,56], V u is the manifold induced by the parametric dependence of the BVP on the input variables).”
Shape optimization for viscous flows by reduced basis methods and free‐form deformation (2012, methodology): “With the above definitions of the RB spaces, the following LBB condition [34, 35] holds:”
On the stability of the reduced basis method for Stokes equations in parametrized domains (2007, background): “are (i) the use of a great number of geometrical parameters, (ii) the non-affine formulation for Stokes reduced basis problem ([28]) and (iii) the study of a posteriori error bounds for Stokes equations.”
POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder (2017, unknown): “The third order tensor Cijk is stored [30,31] to deal with the non-linear term in the present work.”