相关论文: Improved a posteriori Error Bounds for Reduced por…
In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient…
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…
Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in…
A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the appropriate canonical momenta, the model is recast into a coupled…
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale…
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
We present a gradient-based identification algorithm to identify the system matrices of a linear port-Hamiltonian system from given input-output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal…