Related papers: Truncation Error Estimation in the p-Anisotropic D…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…
Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This work is an attempt to develop an approximate scheme for estimating the volume-based truncation errors in the finite volume analysis of laminar flows. The volume-based truncation error is the net flow error across the faces of a control…
We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence free constraint of the magnetic…
The article starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates $L_p([0,T])$ approximations of sub-Gaussian random signals. Explicit truncation error…
This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
In highly diffusion regimes when the mean free path $\varepsilon$ tends to zero, the radiative transfer equation has an asymptotic behavior which is governed by a diffusion equation and the corresponding boundary condition. Generally, a…
Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. While it is possible to achieve accurate predictions using direct solution of the compressible Navier-Stokes equations,…
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…
We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian…
We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially…
In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…