Related papers: A-priori error estimation for space-time Galerkin …

We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant…

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…

In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the…

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave…

In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residual-based a-posteriori error bound on a space-time level and…

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

This work establishes a novel, unified theoretical framework for a class of high order embedded boundary methods, revealing that the Reconstruction for Off-site Data (ROD) treatment shares a fundamental structure with the recently developed…

In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…

In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully…

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexity of the model. In this work, we propose a multidimensional…

We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order discontinuous Galerkin temporal discretizations.…

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…