← Back to Search

Get Citationsy

# On Finite Element Methods For 3D Time-Dependent Convection-Diffusion-Reaction Equations With Small Diffusion

V. John, E. Schmeyer

Published 2008 · Mathematics

Save to my Library

Download PDF

Download via 🐼 PaperPanda
Download via oaDOI
Download via OAB
Download via LibKey
Download via Google
Google Scholar

Analyze on Scholarcy
Visualize in Litmaps
Share

Reduce the time it takes to create your bibliography by a factor of 10 by using the world’s favourite reference manager

Time to take this seriously.

The paper studies finite element methods for the simulation of time-dependent convection-diffusion-reaction equations with small diffusion: the SUPG method, a SOLD method and two types of FEM-FCT methods. The methods are assessed, in particular with respect to the size of the spurious oscillations in the computed solutions, at a 3D example with nonhomogeneous Dirichlet boundary conditions and homogeneous Neumann boundary conditions.

This paper references

10.1016/0021-9991(79)90051-2

Fully multidimensional flux-corrected transport algorithms for fluids

S. Zalesak (1979)

10.1016/0045-7825(86)90003-4

Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations

T. Tezduyar (1986)

10.1090/S0025-5718-1987-0890252-8

Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods

Claes Johnson (1987)

10.1002/FLD.1650071007

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

R. Löhner (1987)

10.1016/0045-7825(88)90108-9

A consistent approximate upwind Petrov—Galerkin method for convection-dominated problems

A. C. Galeão (1988)

10.1016/0045-7825(82)90071-8

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

A. Brooks (1990)

10.1016/0045-7825(91)90231-T

Feedback Petrov-Galerkin methods for convection-dominated problems

E. G. D. D. Carmo (1991)

10.1007/978-3-0348-8629-1_3

Scalar Conservation Laws

R. LeVeque (1992)

10.1016/0045-7825(93)90213-H

A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation

R. Codina (1993)

10.1016/0045-7825(95)00844-9

Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods

T. Hughes (1995)

10.1016/0898-1221(94)00237-F

Necessary L2-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems

M. Stynes (1995)

10.1137/0733033

High-resolution conservative algorithms for advection in incompressible flow

R. LeVeque (1996)

10.1007/978-3-662-03206-0

Numerical Methods for Singularly Perturbed Differential Equations

H. Roos (1996)

10.1007/S002110050309

Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems

V. John (1997)

10.1016/S0045-7825(96)01108-5

A stable Petrov-Galerkin method for convection-dominated problems

R. C. Almeida (1997)

10.1016/S0045-7825(97)00206-5

Comparison of some finite element methods for solving the diffusion-convection-reaction equation

R. Codina (1998)

10.1016/S0045-7825(00)00190-0

On an Improved Unusual Stabilized Finite Element Method for theAdvective-Reactive-Diffusive Equation

L. P. Franca (1999)

10.1051/M2AN:1999145

Stabilization of Galerkin approximations of transport equations by subgrid modelling

J. Guermond (1999)

10.1007/S007910050051

Large Eddy Simulation and the variational multiscale method

T. Hughes (2000)

10.1016/S0045-7825(00)00177-8

On stabilized finite element methods for linear systems of convection-diffusion-reaction equations

R. Codina (2000)

10.1007/S10092-001-8180-4

A finite element pressure gradient stabilization¶for the Stokes equations based on local projections

R. Becker (2001)

10.1016/S0045-7825(02)00318-3

Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation

E. Burman (2002)

10.1007/S007910100068

Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales

R. Codina (2002)

10.1006/JCPH.2001.6955

Flux correction tools for finite elements

D. Kuzmin (2002)

10.1016/S0045-7825(02)00222-0

Stabilized finite element methods with shock capturing for advection–diffusion problems

T. Knopp (2002)

10.1016/S0045-7825(02)00217-7

A simple subgrid scale stabilized method for the advection–diffusion-reaction equation

G. Hauke (2002)

10.1115/1.3424474

The finite element method for elliptic problems

P. G. Ciarlet (2002)

10.1016/S0045-7825(03)00292-5

A new stabilized finite element formulation for scalar convection–diffusion problems: the streamline and approximate upwind/Petrov–Galerkin method

E. G. D. D. Carmo (2003)

10.1007/978-88-470-2089-4_52

The discrete maximum principle for stabilized finite element methods

E. Burman (2003)

10.1007/S00791-003-0120-1

MooNMD – a program package based on mapped finite element methods

V. John (2004)

10.1016/J.APNUM.2003.10.002

Finite element analysis of convection dominated reaction-diffusion problems

A. C. Galeão (2004)

10.1016/J.CMA.2004.01.015

A new upwind function in stabilized finite element formulations, using linear and quadratic elements for scalar convection–diffusion problems

E. G. D. D. Carmo (2004)

10.1016/J.CMA.2003.12.032

Edge stabilization for Galerkin approximations of convection?diffusion?reaction problems

E. Burman (2004)

10.1016/J.CMA.2004.01.026

Stability of the SUPG finite element method for transient advection-diffusion problems

P. Bochev (2004)

10.1145/992200.992206

Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method

T. Davis (2004)

10.1002/0470091355.ECM069

Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces

T. Tezduyar (2004)

10.1016/J.CMA.2004.05.009

High-resolution FEM?FCT schemes for multidimensional conservation laws

D. Kuzmin (2004)

10.1002/0470091355

Encyclopedia of computational mechanics

Erwin Stein (2004)

Flux-corrected transport : principles, algorithms, and applications

D. Kuzʹmin (2005)

10.1016/J.CMA.2004.06.004

Fourier analysis of semi-discrete and space–time stabilized methods for the advective–diffusive–reactive equation: I. SUPG

Guillermo Hauke (2005)

10.1137/030601533

A Finite Element Variational Multiscale Method for the Navier-Stokes Equations

V. John (2005)

10.1090/S0025-5718-05-01761-8

Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence

E. Burman (2005)

10.1007/3-540-27206-2_6

Algebraic Flux Correction I. Scalar Conservation Laws

D. Kuzmin (2005)

10.22028/D291-26320

A comparison of spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. - Part I

V. John (2005)

10.1051/M2AN:2007038

A UNIFIED CONVERGENCE ANALYSIS FOR LOCAL PROJECTION STABILISATIONS APPLIED TO THE OSEEN PROBLEM

G. Matthies (2006)

10.1016/J.CMA.2005.10.006

A two-level variational multiscale method for convection-dominated convection-diffusion equations

V. John (2006)

10.1016/J.CMA.2005.07.017

Residual-based stabilized higher-order FEM for advection-dominated problems

G. Lube (2006)

10.1007/S10778-006-0109-9

On large Eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows

V. John (2006)

10.1137/050631227

Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method

M. Braack (2006)

10.1504/IJCSM.2007.016534

On the performance of SOLD methods for convection-diffusion problems with interior layers

V. John (2007)

10.1002/FLD.1484

YZβ discontinuity capturing for advection-dominated processes with application to arterial drug delivery

Y. Bazilevs (2007)

10.1016/J.CMA.2006.11.013

On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review

V. John (2007)

10.1016/J.CMA.2006.07.011

Stabilized finite element methods for the generalized Oseen problem

M. Braack (2007)

Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.

G. Matthies (2008)

10.1016/J.CMA.2007.08.019

A space-time formulation and improved spatial reconstruction for the "divide-and-conquer" multiscale method

V. Gravemeier (2008)

10.1016/J.CMA.2007.12.019

On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part II – Analysis for P1 and Q1 finite elements

V. John (2008)

10.1016/J.CES.2008.05.004

Simulations of Population Balance Systems with One Internal Coordinate using Finite Element Methods

V. John (2009)

10.1016/j.jcp.2008.12.011

Explicit and implicit FEM-FCT algorithms with flux linearization

D. Kuzmin (2009)

This paper is referenced by

10.1016/j.camwa.2021.02.010

Numerical and experimental examination of the retention of magnetic nanoparticles in magnetic chromatography

Jan E. Marquardt (2021)

10.1016/J.CMA.2021.113909

Fully decoupled, linear and positivity-preserving scheme for the chemotaxis–Stokes equations

Xueling Huang (2021)

10.1016/j.aml.2020.106932

Existence of solutions of a finite element flux-corrected-transport scheme

V. John (2021)

Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Convection-Diffusion Problems

Xianping Li (2021)

10.1016/J.CAM.2021.113672

Eulerian-Lagrangian and Eulerian-Eulerian approaches for the simulation of particle-laden free surface flows using the lattice Boltzmann method

Václav Heidler (2021)

10.1016/J.CAMWA.2020.08.028

Flexible goal-oriented adaptivity for higher-order space-time discretizations of transport problems with coupled flow

M. Bause (2021)

10.1088/1742-6596/1850/1/012001

Virtual element stabilization of convection-diffusion equation with shock capturing

M. Arrutselvi (2021)

10.5194/GMD-14-2545-2021

Assessment of numerical schemes for transient, finite-element ice flow models using ISSM v4.18

Thiago Dias dos Santos (2021)

10.1016/j.compfluid.2020.104525

Locally bound-preserving enriched Galerkin methods for the linear advection equation

D. Kuzmin (2020)

10.1080/10407790.2020.1777764

A two-dimensional finite element recursion relation for the transport equation using nine-diagonal solvers

S. Pirbastami (2020)

A novel equi-dimensional finite element method for flow and transport in fractured porous media satisfying discrete maximum principle and conservation properties

M. Nestola (2020)

10.1134/S0021894420070226

Variational Multiscale Finite-Element Methods for a Nonlinear Convection–Diffusion–Reaction Equation

M. Zhelnin (2020)

10.1007/978-3-030-45168-4_14

Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes

Robin Ahrens (2020)

10.1016/j.cma.2019.112804

Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws

D. Kuzmin (2020)

10.1016/j.amc.2019.124944

A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems

Ji Lin (2020)

10.1016/j.camwa.2020.03.025

Eliminating Gibbs Phenomena: A Non-linear Petrov-Galerkin Method for the Convection-Diffusion-Reaction Equation

P. Houston (2020)

10.1016/j.jhydrol.2020.125062

A mesoscopic coupling scheme for solute transport in surface water using the lattice boltzmann method

Hongda Wang (2020)

10.1016/j.cpc.2019.106941

A positivity preserving characteristic finite element method for solving the transport and convection-diffusion-reaction equations on general surfaces

X. Xiao (2020)

10.1007/978-3-030-30705-9_12

On the Sensitivity to Model Parameters in a Filter Stabilization Technique for Advection Dominated Advection-Diffusion-Reaction Problems

Kayla Bicol (2020)

10.1016/J.JCP.2019.02.051

Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems

Richen Li (2019)

10.1093/imanum/draa053

Higher-order discontinuous Galerkin time discretizations the evolutionary Navier-Stokes equations

N. Ahmed (2019)

10.1016/J.JCP.2019.06.053

A time-space flux-corrected transport finite element formulation for solving multi-dimensional advection-diffusion-reaction equations

D. Feng (2019)

10.1016/J.CMA.2018.12.028

Explicit-in-Time Goal-Oriented Adaptivity

Judit Muñoz-Matute (2019)

10.1080/10407782.2019.1608771

The characteristic RBF-FD method for the convection-diffusion-reaction equation on implicit surfaces

F. Zhao (2019)

10.1016/J.COMPCHEMENG.2019.01.012

Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach

C. Bartsch (2019)

10.1016/J.CES.2019.07.020

Stochastic-deterministic population balance modeling and simulation of a fluidized bed crystallizer experiment

C. Bartsch (2019)

10.1002/cnm.3212

A density-dependent FEM-FCT algorithm with application to modeling platelet aggregation.

N. Danes (2019)

10.1002/cnm.3148

Finite element modeling of near-wall mass transport in cardiovascular flows.

Kirk B Hansen (2019)

10.1007/S10915-019-00944-Z

Adaptive Concepts for Stochastic Partial Differential Equations

A. Prohl (2019)

10.1016/j.cma.2020.113649

A virtual element method for the miscible displacement of incompressible fluids in porous media

L. B. D. Veiga (2019)

10.1007/s00791-018-0290-5

Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

V. John (2018)

10.1016/j.jcp.2018.01.048

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

S. Mabuza (2018)

See more