Related papers: Discrete conservation properties for shallow water…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
The mixed spectral element method (MSEM) is applied to solve the waveguide problem with Bloch periodic boundary condition (BPBC). Based on the BPBC for the original Helmholtz equation and the periodic boundary condition (PBC) for the…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
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 shear shallow water model provides an approximation for shallow water flows by including the effect of vertical shear in the model. This model can be derived from the depth averaging process by including the second order velocity…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
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 consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…
This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear…
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics (MHD) both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from…
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator.…