Related papers: New finite volume element schemes based on a two-l…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
The modern aerodynamic optimization has a strong demand for parametric methods with high levels of intuitiveness, flexibility, and representative accuracy, which cannot be fully achieved through traditional airfoil parametric techniques. In…
We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large…
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic…
This paper focuses on the numerical approximation of the solutions of non-local conservation laws in one space dimension. These equations are motivated by two distinct applications, namely a traffic flow model in which the mean velocity…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order…
This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom…
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…
In this paper we compare a classical finite-difference and a high order finite- volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…