Suppressing spurious oscillations is crucial for designing reliable high-order numerical
schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated …

Sparse-grid methods have recently gained interest in reducing the computational cost of
solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid …

This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for
computing high dimensional partial differential equations (PDEs) and its software …

Discontinuous Galerkin (DG) schemes on unstructured meshes offer the advantages of
compactness and the ability to handle complex computational domains. However, their …

This paper constructs adaptive sparse grid collocation method onto arbitrary order
piecewise polynomial space. The sparse grid method is a popular technique for high …

Physical solutions to the widely used Aw–Rascle–Zhang (ARZ) traffic model and the
adapted pressure ARZ model should satisfy the positivity of density, the minimum and …

The wavelet multiresolution interpolation for continuous functions defined on a finite interval
is developed in this study by using a simple alternative of transformation matrix. The wavelet …

In this paper, we propose a class of adaptive multiresolution (also called the adaptive sparse
grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear …

Abstract The Hamilton-Jacobi (HJ) equations arise in optimal control and many other
applications. Oftentimes, such equations are posed in high dimensions, and this presents …

Simulating general relativistic hydrodynamics (GRHD) presents challenges such as
handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving …