An error analysis of a finite element method for a system of nonlinear advection–diffusion–reaction equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2008.12.035 ◽

2009 ◽

Vol 59 (8) ◽

pp. 1947-1959 ◽

Author(s):

Biyue Liu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Analysis ◽

Diffusion Reaction ◽

Advection Diffusion ◽

Nonlinear Advection ◽

Reaction Equations ◽

Advection Diffusion 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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A new stabilized finite element method for advection-diffusion-reaction equations using quadratic elements

Modelling Fluid Flow ◽

10.1007/978-3-662-08797-8_17 ◽

2004 ◽

pp. 247-266 ◽

Author(s):

Alessandro Corsini ◽

Franco Rispoli ◽

Andrea Santoriello

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Stabilized Finite Element ◽

Stabilized Finite Element Method ◽

Advection Diffusion ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations ◽

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Intrinsic finite element method for advection-diffusion-reaction equations on surfaces

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109827 ◽

2021 ◽

Vol 424 ◽

pp. 109827

Author(s):

Elena Bachini ◽

Matthew W. Farthing ◽

Mario Putti

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Advection Diffusion ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations ◽

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A new stabilized finite element method for advection-diffusion-reaction equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22021 ◽

2015 ◽

Vol 32 (2) ◽

pp. 616-645 ◽

Author(s):

Huoyuan Duan ◽

Fengjuan Qiu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Stabilized Finite Element ◽

Stabilized Finite Element Method ◽

Advection Diffusion ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations ◽

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A fully discrete H 1-Galerkin method with quadrature for nonlinear advection–diffusion–reaction equations

Numerical Algorithms ◽

10.1007/s11075-007-9066-6 ◽

2007 ◽

Vol 43 (4) ◽

pp. 355-383 ◽

Author(s):

M. Ganesh ◽

K. Mustapha

Keyword(s):

Galerkin Method ◽

Diffusion Reaction ◽

Fully Discrete ◽

Advection Diffusion ◽

Nonlinear Advection ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations

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

Journal of Computational Physics ◽

10.1016/j.jcp.2019.06.053 ◽

2019 ◽

Vol 396 ◽

pp. 31-53 ◽

Author(s):

Dianlei Feng ◽

Insa Neuweiler ◽

Udo Nackenhorst ◽

Thomas Wick

Keyword(s):

Finite Element ◽

Finite Element Formulation ◽

Diffusion Reaction ◽

Element Formulation ◽

Advection Diffusion ◽

Flux Corrected Transport ◽

Reaction Equations ◽

Advection Diffusion Reaction Equations

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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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A new nonconforming finite element method for convection dominated diffusion-reaction equations

International Journal of Advances in Engineering Sciences and Applied Mathematics ◽

10.1007/s12572-016-0174-1 ◽

2016 ◽

Vol 8 (4) ◽

pp. 274-283 ◽

Author(s):

Dibyendu Adak ◽

E. Natarajan ◽

Sarvesh Kumar

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Nonconforming Finite Element ◽

Nonconforming Finite Element Method ◽

Convection Dominated ◽

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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Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection–diffusion–reaction problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2021.114027 ◽

2021 ◽

Vol 385 ◽

pp. 114027

Author(s):

Roberto J. Cier ◽

Sergio Rojas ◽

Victor M. Calo

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Reaction ◽

Stabilized Finite Element ◽

Stabilized Finite Element Method ◽

Advection Diffusion ◽

Residual Minimization ◽

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