Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations
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In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-i ...
In this paper we consider reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear and non-linear parabolic partial differential equations. The essential ingredients are Galerkin projection ...
Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientic computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-delity "truth" f ...
Flows having a variable fluid density can be visualized with optical methods. Recently, a background distortion technique, which can be considered a type of Schardin's schlieren #2, was proposed to study the refractive index variation in fluid and hence to ...
This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — mate ...
In this paper we deal with reduced basis techniques applied to Stokes equations. We consider domains with different shape, parametrized by affine and non-affine maps with respect to a reference domain. The proposed method is ideally suited for the repeated ...
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at diff ...
In this thesis we will deal with the creation of a Reduced Basis (RB) approximation of parametrized Partial Differential Equations (PDE) for three-dimensional problems. The the idea behind RB is to decouple the generation and projection stages (Offline/Onli ...
This paper presents numerical simulations of annular laminar film condensation heat transfer in microchannels of different internal shapes. The model, which is based on a finite volume formulation of the Navier-Stokes and energy equations for the liquid ph ...
This work focuses on the approximation of parametric steady Navier-- Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute ...