Related papers: Automatic Variationally Stable Analysis for FE Com…
We propose a low Mach number, Godunov-type finite volume scheme for the numerical solution of the compressible Euler equations of gas dynamics. The scheme combines Klein's non-stiff/stiff decomposition of the fluxes (J. Comput. Phys.…
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…
We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…
In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, we restrict our analysis to triangular meshes with hanging…
We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order $\alpha (1<\alpha<2)$ defined through the fractional Laplacian. The fractional operator of order $\alpha$ is expressed as a…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an…
In this paper subgrid multiscale stabilized finite element method for Advection-Diffusion-Reaction (ADR) equation coupled with Stokes-Darcy flow problem has been studied. Here the advection velocity involved in ADR equation obeys…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…
Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG)…
A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable…
We consider the construction of locally conservative fluxes by means of a simple post-processing technique obtained from the finite element solutions of advection diffusion equations. It is known that a naive calculation of fluxes from…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of…