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

Computer Physics Communications ◽

10.1016/j.cpc.2019.106941 ◽

2020 ◽

Vol 247 ◽

pp. 106941 ◽

Author(s):

Xufeng Xiao ◽

Zihuan Dai ◽

Xinlong Feng

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Positivity Preserving ◽

Convection Diffusion ◽

Characteristic Finite Element ◽

Reaction Equations ◽

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Numerical solution of convection–diffusion–reaction equations by a finite element method with error correlation

AIP Advances ◽

10.1063/5.0050792 ◽

2021 ◽

Vol 11 (8) ◽

pp. 085225

Author(s):

Sadia Akter Lima ◽

Md. Kamrujjaman ◽

Md. Shafiqul Islam

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Solution ◽

Diffusion Reaction ◽

Convection Diffusion ◽

Error Correlation ◽

Reaction Equations ◽

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Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations

Science China Mathematics ◽

10.1007/s11425-015-4992-6 ◽

2015 ◽

Vol 58 (6) ◽

pp. 1327-1348 ◽

Author(s):

ShaoHong Du ◽

XiaoPing Xie

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

Diffusion Reaction ◽

Convection Diffusion ◽

Reaction Equations ◽

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A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations

Journal of Applied Mathematics and Physics ◽

10.4236/jamp.2017.56109 ◽

2017 ◽

Vol 05 (06) ◽

pp. 1301-1319

Author(s):

Tongjun Sun

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

Second Order ◽

Diffusion Reaction ◽

Convection Diffusion ◽

Reaction Equations ◽

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A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems

Journal of Computational Mathematics ◽

10.4208/jcm.1210-m3966 ◽

2013 ◽

Vol 31 (1) ◽

pp. 88-106

Author(s):

Hongfei Fu

Keyword(s):

Finite Element Method ◽

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Diffusion Reaction ◽

Control Problems ◽

Convection Diffusion ◽

Characteristic Finite Element ◽

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A layers capturing type H-adaptive finite element method for convection–diffusion–reaction equations on surfaces

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2019.112792 ◽

2020 ◽

Vol 361 ◽

pp. 112792 ◽

Author(s):

Xufeng Xiao ◽

Jianping Zhao ◽

Xinlong Feng

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Adaptive Finite Element Method ◽

Adaptive Finite Element ◽

Convection Diffusion ◽

Reaction Equations ◽

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A gradient recovery–based adaptive finite element method for convection‐diffusion‐reaction equations on surfaces

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6163 ◽

2019 ◽

Vol 120 (7) ◽

pp. 901-917 ◽

Author(s):

Xufeng Xiao ◽

Xinlong Feng ◽

Zhilin Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Adaptive Finite Element Method ◽

Adaptive Finite Element ◽

Gradient Recovery ◽

Convection Diffusion ◽

Reaction Equations ◽

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A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013071 ◽

2013 ◽

Vol 47 (5) ◽

pp. 1335-1366 ◽

Author(s):

Gabriel R. Barrenechea ◽

Volker John ◽

Petr Knobloch

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Local Projection ◽

Convection Diffusion ◽

Local Projection Stabilization ◽

Reaction Equations ◽

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A robust WG finite element method for convection–diffusion–reaction equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2016.10.029 ◽

2017 ◽

Vol 315 ◽

pp. 107-125 ◽

Author(s):

Gang Chen ◽

Minfu Feng ◽

Xiaoping Xie

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Convection Diffusion ◽

Reaction Equations ◽

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A space-time finite element method based on local projection stabilization in space and discontinuous Galerkin method in time for convection-diffusion-reaction equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125937 ◽

2021 ◽

Vol 397 ◽

pp. 125937

Author(s):

Ziming Dong ◽

Hong Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Diffusion Reaction ◽

Local Projection ◽

Convection Diffusion ◽

Local Projection Stabilization ◽

Reaction Equations

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On enforcing maximum principles and achieving element-wise species balance for advection–diffusion–reaction equations under the finite element method

Journal of Computational Physics ◽

10.1016/j.jcp.2015.09.057 ◽

2016 ◽

Vol 305 ◽

pp. 448-493 ◽

Author(s):

M.K. Mudunuru ◽

K.B. Nakshatrala

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Maximum Principles ◽

The Finite Element Method ◽

Advection Diffusion ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations ◽

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