Port reduction in parametrized component static condensation: approximation and a posteriori error estimation

Port Reduction in Parametrized Component Static Condensation: Approximation and A Posteriori Error Estimation∗

We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are i) efficient empirical port approximation spaces — the dimensions of these spaces may be chosen small in order to reduce the computational cost a...

Port Reduction in Component-Based Static Condensation for Parametrized Problems: Approximation and A Posteriori Error Estimation∗

We introduce a port (interface) approximation and a posteriori error bound framework for a general component–based static condensation method in the context of parameter–dependent elliptic partial differential equations. The key ingredients are i) efficient empirical port approximation spaces — the dimensions of these spaces may be chosen small in order to reduce the computational cost associat...

Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations

Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold” — dimension reduction; efficient and ef...

Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation

In this chapter 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 onto a low-dimensional space associated with a smooth “parametric manifold” — dimension reduction; efficient and effective Greedy and POD-...