相关论文: A Neural Network based Shock Detection and Localiz…

The magnetic flow meter is one of the best possible choice for the measurement of flow rate of liquid metals in fast breeder reactors. Due to the associated complexities in the measuring environment, theoretical evaluation of their…

We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…

In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a…

In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…

High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features, and have traditionally required additional filtering, limiting, or artificial viscosity to avoid solution blow up.…

We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise…

Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level…

Numerically solving magnetohydrodynamic (MHD) equations faces many challenges: avoiding divergence error, maintaining positivity, and satisfying entropy conditions. Among discontinuous Galerkin (DG) schemes, there has been a modal version…

We prove the accuracy of a mixed finite element method for bending dominated shells in which a major part of the membrane/shear strain is reduced, to free up membrane/shear locking. When no part of the membrane/shear strain is reduced, the…

The embedded discontinuous Galerkin (EDG) finite element method for the Stokes problem results in a point-wise divergence-free approximate velocity on cells. However, the approximate velocity is not H(div)-conforming and it can be shown…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…

Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture…

This contribution, Part I in a two-part article series, presents a general-domain version of the FC-SDNN (Fourier Continuation Shock-detecting Neural Network) spectral scheme for the numerical solution of nonlinear conservation laws, which…

We present a non-intrusive model reduction framework for linear poroelasticity problems in heterogeneous porous media using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the…

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…

In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use…

The paper proposes and analyzes an efficient second-order in time numerical approximation for the Allen-Cahn equation, which is a second order nonlinear equation arising from the phase separation model. We firstly present a fully discrete…

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions,…