Related papers: A Globally Conservative Compact Framework for Cons…
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…
In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…
We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation,…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…
This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in [{\em J. Li and Z. Du, A…
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
The stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability of a non-linear scheme in terms of its cor- responding scheme in…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of $\mathbb{R}^3$. We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on…
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…
This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as…