Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications
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The objective of this work is to develop a numerical framework to perform rapid and reliable simulations for solving parametric problems in domains represented by networks and to extend the classical reduced basis method. Aimed at this scope, we propose tw ...
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 ...
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 ...
This master thesis aims at the development, analysis and computer implementation of effcient numerical methods for the solution of optimal control problems based on parametrized partial differential equations. Our goal isfto develop a new approach based on ...
In this paper we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the compu ...
In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...
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 ...
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low dimensional s ...
In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the ...
We propose the reduced basis method for the solution of parametrized optimal control problems described by parabolic partial differential equations in the unconstrained case. The method, which is based on an off-line–on-line decomposition procedure, allows ...
