Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

Discontinuous Galerkin (DG) methods are a class of finite element methods using
discontinuous basis functions, which are usually chosen as piecewise polynomials. Since …

Simulations of flow for a discrete-fracture model in fractured porous rocks have gradually
become more practical, as a consequence of increased computer power and improved …

Research on conjugated radiation-conduction (CRC) heat transfer in participating media is
of vital scientific and engineering significance due to its extensive applications. Appropriate …

We present a new adaptive fluid simulation method that captures a high resolution surface
with precise dynamics, without an inefficient fine discretization of the entire fluid volume …

In this article, we present a new high‐order discontinuous Galerkin (DG) method, in which
neither a penalty parameter nor a stabilization parameter is needed. We refer to this method …

We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed
based on a first-order hyperbolic advection–diffusion formulation of the target governing …

This paper concerns an error analysis of the space semidiscrete scheme for the Richards'
equation modeling flows in variably saturated porous media. This nonlinear parabolic partial …

This article is concerned with a two-dimensional singularly perturbed convection-reaction-
diffusion interface problem. In the considered problem, the convection and reaction …

This paper is concerned with the convergence and superconvergence of the local
discontinuous Galerkin (LDG) finite element method for nonlinear fourth-order boundary …