Hybridized SUPG and Upwind numerical schemes for convection dominated diffusion problems

SUPG reduced order models for convection-dominated convection-diffusion-reaction equations

This paper presents a Streamline-Upwind Petrov–Galerkin (SUPG) reduced order model (ROM) based on Proper Orthogonal Decomposition (POD). This ROM is investigated theoretically and numerically for convection-dominated convectiondi usion-reaction equations. The SUPG finite element method was used on realistic meshes for computing the snapshots, leading to some noise in the POD data. Numerical ana...

Numerical Methods for Scalar Convection-Dominated Problems

Convection-diffusion problems, SDFEM/SUPG and a priori meshes

This paper aims to give the reader a summary of current understanding of the streamlinediffusion finite element method (SDFEM), as applied to linear steady-state convection-diffusion problems. Towards this end, we begin with a brief description of the nature of convectiondiffusion problems: the structure of their solutions will be examined, with special emphasis on the main phenomena of exponen...

Hybridized Discontinuous Galerkin Method for Convection-Diffusion-Reaction Problems

In this paper, we propose a new hybridized discontinuous Galerkin method for the convection-diffusion-reaction problems with mixed boundary conditions. The coercivity of the convection-reaction part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H1-seminorm. Furthermore, we show that the approximate solution of our scheme is close to that of t...

Numerical Methods for Solving Convection-Diffusion Problems

Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective transport of individual phases. Moreover, for compressible media, the pressure equation itself is just a time-dependent convection-diffusion equation. For differen...