A Modified CUI Scheme for Convection-Dominated Equations

Multiscale Analysis for Convection Dominated Transport Equations

In this paper, we perform a systematic multiscale analysis for convection dominated transport equations with a weak diffusion and a highly oscillatory velocity field. The paper primarily focuses on upscaling linear transport equations. But we also discuss briefly how to upscale two-phase miscible flows, in which case the concentration equation is coupled to the pressure equation in a nonlinear ...

The Eafe Scheme and Cwdd Method for Convection-dominated Problems

A monotone finite element scheme for convection-diffusion equations

A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an M -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. A...

A weighted mass explicit scheme for convection-diffusion equations

An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method’s weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we st...

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...