相关论文: A robust second-order low-rank BUG integrator base…

A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [38].…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

We present a robust and accurate numerical method to solve the modified Buckley-Leverett equation in two-phase porous media flow with dynamic capillary pressure effect. A symmetric interior penalty discontinuous Galerkin method is used to…

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…

We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A…

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…

The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…

Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes allows increased computational efficiency while achieving the…

This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…

Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this paper, we firstly discuss the boundedness of a local bi-cubic Lagrange…

This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equation under minimal regularity assumptions on general…

This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an optimal order of error estimates for the exact solution in…

In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…

The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…

The discontinuous Galerkin (DG) time-stepping method applied to abstract evolution equation of parabolic type is studied using a variational approach. We establish the inf-sup condition or Babu\v{s}ka--Brezzi condition for the DG bilinear…

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper…

In this paper, by introducing a reconstruction operator based on the Legendre moments, we construct a reduced discontinuous Galerkin (RDG) space that could achieve the same approximation accuracy but using fewer degrees of freedom (DoFs)…

On the basis of the previous work by Tang \& Zhang (Appl. Math. Comput. 323, 2018, p. 204--219), in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations.…

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model…

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static,…