. Dans-les, cette régénération thermique s'effectue après quelques centaines de kilomètres environ. Cependant, si les températurestempératures`températuresà ce niveau de la ligne d'´ echappement augmentent l'efficacité du catalyseur (température d'activation du catalyseur atteinte plus rapidement), l'exotherme engendré par la régénération provoque des fuites importantes d'ammoniac, composé fortement odorant

U. Ainsi and S. Catalyseur, excédent de NH 3 issu du premier catalyseur SCR-FAP etéviteretéviter leur rejet dans l'environnement. Une conséquence non négligeable est que l'on pourra de cette façon, réduiré egalement l'excédent de NO x non traité par le premierélémentpremierélément catalytique et améliorer l'efficacité globale de l'architecture. Cette architecture nécessite donc un moyen de contrôle spécifique permettant d'´ eviter les fuites en ammoniac issue des catalyseurs mais aussi d'en optimiser le fonctionnement globaì a travers la gestion des

. Description-de-la-méthode, Une stratégie de contrôle du catalyseur SCR-FAP (seul dans l'architecture) est proposée Elle consiste simplement en la diminution voire l'arrêt de l'injection d'urée dans la ligne d'´ echappement avant et pendant les phases de régénération permettant de prévenir d'´ eventuelles fuites d'ammoniac. Un système de mesure de résistance fluidique (cf

. Commentaire, Nous pouvons faire le constat suivant : cette méthode a pour inconvénient d'´ eviter lesémissions lesémissions polluantes (en diminuant l'apport en NH 3 ) en dépit desémissionsdesémissions de NO x . En effet, pendant les phases de régénération o` u l'on réduit l'apport en ammoniac, l'efficacité du catalyseur est détériorée, et on ne traite plus les NO x de façon efficace

S. Scr, Nous proposons de tirer profit du catalyseur en aval de l'architecture décrite en Figure 5.3 afin de contrôler au mieux et de façon continue, les NO x et le NH 3 , en adaptant la stratégie d'injection d'urée suivant les plages de température d'entrée dans lesquelles on se trouve. Cette procédure s'effectue en régulant demanì ere précise chacun des stocks de NH 3 des catalyseurs SCR-FAP et SCR de la ligne d'´ echappement. Cela permet d'´ eviter la pollution en NH 3 tout en préservant l'efficacité de traitement des NO x . Dans cette application, p.84

R. Snow, G. Cavatatio, D. Dobson, and C. Montreuil, Calibration of a LNT-SCR Diesel Aftertreatment System SAE Technical Paper, pp.10-4271, 1244.

J. Theis and E. Gulari, A LNT+SCR System for Treating the NOx Emissions from a Diesel Engine, SAE Technical Paper Series, pp.10-4271, 2006.
DOI : 10.4271/2006-01-0210

A. Ketfi-cherif, D. Von-wissel, S. Beurthey, M. A. Sorine, P. Darcy et al., Modeling and Control of a NOx Trap Catalyst SAE Technical Paper Modelling of a Lean NOx-Trap System with NO/NO 2 Differentiation and Sulfur Poisoning, SAE Int. J. Fuels Lubr, vol.42714271, issue.32, pp.414-424102010, 1199.

J. R. Theis, J. A. Ura, and R. W. Mccabe, The Effects of Sulfur Poisoning and Desulfation Temperature on the NOx Conversion of LNT+SCR Systems for Diesel Applications, SAE International Journal of Fuels and Lubricants, vol.3, issue.1, pp.1-15, 2010.
DOI : 10.4271/2010-01-0300

D. Di-penta and . Damiano, di-penta@renault.com FR TCR RUC T65 -1 Avenue du Golf -78288 Guyancourt - France Phone, pp.33-34

. Pierre-alexandre, Bliman pierre-alexandre.bliman@inria.fr INRIA Rocquencourt -Domaine de Voluceau -BP105 - 78153 Le Chesnay cedex -France Phone

M. Sorine and M. , sorine@inria.fr INRIA Rocquencourt -Domaine de Voluceau -BP105 - 78153 Le Chesnay cedex -France Phone, pp.33-34

Y. Joshi, P. Jiang, S. Flörchinger, and . Ogunwumi, Two-dimensional transient monolith model for selective catalytic reduction using vanadia-based catalyst. SAE technical paper series, pp.2008-2036, 2008.

A. Lindholm, N. W. Currier, J. Li, A. Yezerets, and L. Olsson, Detailed kinetic modeling of NO x storage and reduction with hydrogen as the reducing agent and in the presence of CO 2 and H 2 O over a Pt?Ba/Al catalyst, Journal of catalysis, 2008.

A. P. York, M. Ahmadinejad, T. C. Watling, and A. P. Walker, Modeling of the Catalized Continuously Regenerated Diesel Particulate Filter (CCR-DPF) System: Model Development and Passive Regeneration Studies. SAE Technical Paper, pp.2007-2008, 2007.

D. Chatterjee, P. Koci, V. Schmeisser, and M. Marek, Modelling of NOx Storage + SCR Exhaust Gas Aftertreatment System with Internal Generation of Ammonia, SAE International Journal of Fuels and Lubricants, vol.3, issue.1, pp.500-522, 2010.
DOI : 10.4271/2010-01-0887

P. Marie-luce, D. Bliman, M. Di-penta, R. /. Sorine, and . Inria, Reduced Order Models for Hybrid Diesel After-treatment Architecture with NO/NO 2 Differentiation, 2012.
DOI : 10.3182/20120711-3-be-2027.00215
URL : https://hal.inria.fr/hal-00682731/document

D. Terribile, J. Llorca, M. Boaro, C. De-leitenburg, G. Dolcetti et al., Fast Oxygen Uptakes/Release over a New CeO x Phase, Chemical Communications, vol.17, pp.1897-1898, 1998.

J. Parks and V. Prikhodko, Ammonia Production and Utilization in Hybrid LNT+SCR System. SAE Technical Paper, 2009.
DOI : 10.4271/2009-01-2739

J. Parks, S. Huff, J. Pihl, and J. S. Choi, Nitrogen Selectivity in Lean NOx Trap Catalysis with Diesel Engine In-Cylinder Regeneration, SAE Technical Paper Series, pp.2005-2006, 2005.
DOI : 10.4271/2005-01-3876

J. C. Wurzenberg and R. Wanker, Multi-Scale SCR Modeling , 1D Kinetic Analysis and 3D System Simulation. SAE Technical paper series, 2005.

I. Lietti, P. Nova, and . Forzatti, Mechanistic Aspects of the Reduction of Stored NO x over Pt?Ba/Al 2 O 3 Lean NO x Trap Systems, Catalysis Today, 2008.

P. Kokotovi´ckokotovi´c, H. Khalil, and J. O-'reily, Singular Perturbation in Control, Analysis and Design. SIAM, 1999.

W. Chatlatanagulchai, K. Yaovaja, S. Rhienprayoon, and K. Wannatong, Air-Fuel Ratio Regulation with Optimum Throttle Opening in Diesel-Dual-Fuel Engine, SAE Technical Paper Series, pp.2010-2011, 2010.
DOI : 10.4271/2010-01-1574

]. A. Bibliographie1, N. W. Lindholm, J. Currier, A. Li, L. Yezerets et al., Detailed kinetic modeling of NO x storage and reduction with hydrogen as the reducing agent and in the presence of CO 2 and H 2 O over a Pt?Ba/Al catalyst, Journal of catalysis, 2008.

L. Lietti, I. Nova, and P. Forzatti, Mechanistic Aspects of the Reduction of Stored NO x over Pt?Ba/Al 2 O 3 Lean NO x Trap Systems, Catalysis Today, 2008.

L. Lietti, I. Nova, and P. Forzatti, Role of Ammonia in the Reduction by Hydrogen of NO x Stored over Pt?Ba/Al 2 O 3 Lean NO x Trap Catalyst, Journal of catalysis, 2008.

D. Di-penta, Modélisation, surveillance et contrôle des niveaux de polluants résidant dans les groupes motopropulseursàmotopropulseursà faiblesémissionsfaiblesémissions, 2007.

A. Ketfi-cherif, Modélisation mathématique d'organes de véhicules automobilesàautomobilesà basse consommation. Applications en simulation, estimation et commande, 1999.

M. Schaefer, L. Hofmann, P. Girot, and R. Rohe, Investigation of NO x -and PMreduction by a Combination of SCR-catalyst and Diesel Particuate Filter for Heavy- Duty Diesel Engine, SAE Int. J. Fuels Lubr, pp.386-398, 2009.

A. P. York, M. Ahmadinejad, T. C. Watling, and A. P. Walker, Modeling of the Catalized Continuously Regenerated Diesel Particulate Filter (CCR-DPF) System : Model Development and Passive Regeneration Studies. SAE Technical Paper, pp.2007-2008, 2007.

M. Milh and H. Westberg, Reduction of NO 2 Stored in a Commercial Lean NO x Trap at Low Temperatures, Topics in catalysis, 2007.

O. Inderwildi, Multiscale modelling for automotive exhaust-gas after-treatment, from the quantum chemistry to the engineering level, 2005.

G. F. Oster and A. S. Perelson, Chemical reaction dynamics, Archive for Rational Mechanics and Analysis, vol.45, issue.3, 1971.
DOI : 10.1002/ijch.197300041

H. Eyring, The Activated Complex in Chemical Reactions, The Journal of Chemical Physics, vol.9, issue.2, pp.107-115, 1935.
DOI : 10.1063/1.1749291

D. J. Winzor and C. M. Jackson, Interpretation of the temperature dependence of equilibrium and rate constants, Journal of Molecular Recognition, vol.246, issue.5, pp.389-407, 2006.
DOI : 10.1042/bj1460409

P. Erdi and J. Tóth, Mathematical models of chemical reactions : Theory and applications of deterministic and stochastic models, 1989.

M. Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors???I. The deficiency zero and deficiency one theorems, Chemical Engineering Science, vol.42, issue.10, pp.2229-2268, 1987.
DOI : 10.1016/0009-2509(87)80099-4

A. N. Tikhonov, Systems of differential equations containing small parameters multiplying the derivatives, Mat. Sborn, vol.31, pp.575-586, 1952.

P. Kokotovi´ckokotovi´c, H. Khalil, and J. O-'reily, Singular Perturbation in Control, Analysis and Design. SIAM, 1999.

C. Lobry, T. Sari, and S. Touhami, On Tykhonov's theorem for convergence of solutions of slow and fast systems, Electronic Journal of Differential Equations, pp.1-22, 1998.

W. S. Epling, L. E. Campbell, A. Yezerets, N. W. Currier, and J. E. Parks, Overview of the Fundamental Reactions and Degradation Mechanisms of NOx Storage/Reduction Catalysts, Catalysis Reviews, vol.38, issue.2, pp.163-245, 2004.
DOI : 10.1002/aic.690330212

P. Forzatti, L. Castoldi, L. Lietti, I. Nova, and E. Tronconi, Identification of the Reaction Networks of the NO x Storage :Reduction in Lean NO x Trap Systems, 2007.

Y. Wang, S. Raman, and J. W. Grizzle, Dynamic modeling of a lean NO x trap for a lean burn engine control, Proc., IEEE ACC, 1999.

J. Kim, J. Sun, I. Kolmanovsky, and J. Koncsol, A Phenomenological Control Oriented Lean NOx Trap Model, SAE Technical Paper Series, 2003.
DOI : 10.4271/2003-01-1164

A. Ketfi-cherif, D. Von-wissel, S. Beurthey, and M. Sorine, Modeling and Control of a NO x Trap catalyst, SAE Technical Paper, 1199.

D. Di-penta and R. Sas, NO x trap : Modèle de chargement NO x embarqué, 2008.

A. Joshi, Y. Jiang, P. Flörchinger, and S. Ogunwumi, Two-dimensional transient monolith model for selective catalytic reduction using vanadia-based catalyst. SAE technical paper series, pp.2008-2036, 2008.
DOI : 10.4271/2008-28-0022

S. Hackenberg and M. Ranalli, Ammonia on a LNT : Avoid th eFormation or Take Advantage of It. SAE Technical Paper, 1239.

L. Olsson and B. Andersson, Kinetic modeling in automotive catalysis, Topics in catalysis, 2004.
DOI : 10.1023/b:toca.0000024337.50617.8e

A. Manigrasso, P. Darcy, and P. Costa, Modeling of a Lean NO x Trap System with NO/NO 2 Differentiation, SAE INT. J. Fuels Lubr, pp.414-424, 2010.

A. Lindholm, N. W. Currier, A. Yezerets, and L. Olsson, A kinetic study of NO x reduction over PtSiO 2 model catalyst with hydrogen as the reducing agent, Topics in catalysis, 2007.

D. Terribile, J. Llorca, M. Boaro, C. De-leitenburg, G. Dolcetti et al., Fast Oxygen Uptakes/Release over a New CeO x Phase, Chemical Communications, vol.17, pp.1897-1898, 1996.

M. Sharma, K. Kabin, M. P. Harold, and V. Balakotaiah, Modeling of NOx Storage and Reduction for Diesel Exhaust Emission Control, SAE Technical Paper Series, 2005.
DOI : 10.4271/2005-01-0972

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-107, 1961.
DOI : 10.1115/1.3658902
URL : http://www.eecs.tufts.edu/~khan/Courses/Spring2012/EE194/Lecs/KalmanBucy1961.pdf

D. G. Luenberger, Observing the State of a Linear System, IEEE Transactions on Military Electronics, vol.8, issue.2, pp.74-80, 1964.
DOI : 10.1109/TME.1964.4323124

D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971.
DOI : 10.1109/TAC.1971.1099826

G. Besançon, Nonlinear Observers and Applications, 2007.

J. Wang, Smooth In-Cylinder Lean-Rich Combustion Switching Control for Diesel Engine Exhaust-Treatment System Regenerations, SAE International Journal of Passenger Cars - Electronic and Electrical Systems, vol.1, issue.1, pp.340-348, 2008.
DOI : 10.4271/2008-01-0979

S. Nakagawa, T. Hori, and M. Nagano, A New Feedback Control of a Lean Nox Trap Catalyst, SAE Technical Paper Series, pp.2004-2005, 2004.
DOI : 10.4271/2004-01-0527

D. Sunohara, S. Khoketsu, S. Nakayama, K. Tanabe, M. Murata et al., Control of Rich Spike with Adaptive Estimation of Stored NOx in Lean NOx Trap for a Diesel Engine, SAE Technical Paper Series, 1090.
DOI : 10.4271/2005-01-1090

A. Ketfi-cherif, Modélisation mathématique d'organes de véhicules automobilesà automobilesà basse consommation. Applications en simulation, estimation et commande, 1999.

J. F. Bonnans, C. Jeanbrun, A. Ketfi-cherif, and D. V. Wissel, Optimal control of a gasoline-fueled car engine under pollution constraints, ESAIM Proceedings, 1999.

J. A. Dumesic, N. Topsoe, H. Topsoe, Y. Chen, and T. Slabiak, Kinetics of Selective Catalytic Reduction of Nitric Oxide by Ammonia over Vanadia/Titannia, Journal of catalysis, 1996.

J. H. Baik, S. D. Yim, I. Nam, J. Lee, B. K. Cho et al., Control of NO x emissions from Diesel engine by selective catalytic reduction (SCR) with urea, Topics in catalysis, 2004.

I. Nova, C. Ciardelli, E. Tronconi, D. Chatterjee, and M. Weibel, NH 3 ?NO/NO 2 SCR for Diesel Exhausts After Treatment : Mechanism and Modelling of a Catalytic Converter, Topics in catalysis, 2007.

G. Lüder and K. S. Narendra, An adaptive observer and identifier for a linear system, IEEE Trans. on Automatic control, vol.18, pp.496-499, 1973.

G. Kreisselmeier, Adaptive observers with exponential rate of convergence, IEEE Transactions on Automatic Control, vol.22, issue.1, pp.2-8, 1977.
DOI : 10.1109/TAC.1977.1101401

G. Bastin and M. Gevers, Stable adaptive observers for nonlinear time-varying systems, IEEE Transactions on Automatic Control, vol.33, issue.7, pp.650-658, 1988.
DOI : 10.1109/9.1273

R. Marino and P. Tomei, Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems, IEEE Transactions on Automatic Control, vol.40, issue.7, pp.1300-1304, 1995.
DOI : 10.1109/9.400471

R. Marino and P. Tomei, Nonlinear control design, 1995.

R. Rajamani and J. K. Hendrick, Adaptive observers for active automotive suspensions: theory and experiment, IEEE Transactions on Control Systems Technology, vol.3, issue.1, pp.86-93, 1995.
DOI : 10.1109/87.370713

Y. M. Cho and R. Rajamani, A systematic approach to adaptive observer synthesis for nonlinear systems, IEEE Trans. on Automatic control, vol.42, issue.4, pp.534-537, 1997.

G. Besançon, Remarks on nonlinear adaptive observer design. Systems and Control Letters, pp.271-280, 2000.

Q. Zhang, Adaptive observer for mimo linear time varying systems, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072520

Q. Zhang and B. Delyon, A new approach to adaptive observer design for mimo systems, ACC, 2001.

Q. Zhang and A. Xu, Implicit adaptive observers for a class of nonlinear systems, ACC, 2001.

B. Marx, D. Georges, and D. Koenig, Optimal sensor/actuator location for descriptor systems using Lyapunov-like equations, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.4541-4542, 2002.
DOI : 10.1109/CDC.2002.1185090
URL : https://hal.archives-ouvertes.fr/hal-00232856

D. Georges, The use of observability and controllability gramians or function for optimal sensor and actuator location in finite dimensionnal systems, Proc. of the 34th IEEE Conference on Decision and Control, pp.3319-3324, 1995.

S. Leleu, H. Abou-kandil, and Y. Bonnassieux, Piezoelectric actuators and sensors location for active control of flexible structures, IEEE trans. on Instrumentation and Measurement, pp.1577-1582, 2001.

K. Hassan and . Khalil, Nonlinear Systems, 1996.
URL : https://hal.archives-ouvertes.fr/hal-01698610

M. David, Modélisation réduite de système de post-traitement diesel en vue de la commande, 2009.

R. Bosch-gmbh, Procedure and control unit to operate an integrated SCR/DPF system, Institut National de la Propriété Industrielle, 2005.

R. Aris, Introduction to the Analysis of Chemical Reactors, 1965.

R. Snow, G. Cavatatio, D. Dobson, C. Montreuil, and R. Hammerle, Calibration of a LNT-SCR Diesel Aftertreatment System, SAE Technical Paper Series, 1244.
DOI : 10.4271/2007-01-1244

]. C. Enderle, G. Vent, and M. Paule, Bluetec Diesel Technology -Clean, Efficient and Powerful. SAE Technical Paper, pp.2008-2009, 2008.
DOI : 10.4271/2008-01-1182

C. M. Schär, C. H. Onder, H. P. Geering, and M. Elsener, Control of a Urea SCR Catalytic Converter System for a Mobile Heavy Duty Diesel Engine, SAE Technical Paper Series, 2003.
DOI : 10.4271/2003-01-0776

J. Theis and E. Gulari, A LNT+SCR System for Treating the NOx Emissions from a Diesel Engine, SAE Technical Paper Series, pp.2006-2007, 2006.
DOI : 10.4271/2006-01-0210

J. R. Theis, J. A. Ura, and R. W. Mccabe, The Effects of Sulfur Poisoning and Desulfatation Temperature on the NO x Conversion of LNT+SCR Systems for Diesel Applications, SAE Int. J. Fuels Lubr, pp.1-15, 2010.

J. Parks and V. Prikhodko, Ammonia Production and Utilization in Hybrid LNT+SCR System. SAE Technical Paper, 2009.

L. Cao, J. L. Ratts, A. Yezerets, N. W. Currier, J. M. Caruthers et al., Kinetic Modeling of NO x Storage/Reduction on Pt?Ba/Al 2 O 3 Monolith Catalysts, Industrial & Engineering Chemistry, 2008.

Q. Song and G. Zhu, Model-based Close-loop Control of Urea SCR Exhaust Aftertreatment System forDiesel Engine, SAE Technical Paper Series, 2002.

L. Hofmann, K. Rusch, S. Fischer, and B. Lemire, Onboard Emissions Monitoring on a HD Truck with an SCR System Using Nox Sensors, SAE Technical Paper Series, 1290.
DOI : 10.4271/2004-01-1290

A. Varma, C. Georgakis, N. R. Amundson, and R. Aris, Computational methods for the tubular chemical reactor, Computer Methods in Applied Mechanics and Engineering, vol.8, issue.3, pp.319-330, 1976.
DOI : 10.1016/0045-7825(76)90021-9

Y. Cho and B. Joseph, Reduced-order steady-state and dynamic models for separation processes. Part I. Development of the model reduction procedure, AIChE Journal, vol.29, issue.2, pp.261-269, 1983.
DOI : 10.1002/aic.690290213

J. Coron, Quelques résultats sur la commandabilité et la stabilisation des systèmes non linéaires, 1999.

M. F. Hsieh and J. Wang, Nonlinear model predictive control of lean NO<inf>x</inf> trap regenerations, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009.
DOI : 10.1109/CDC.2009.5399692

D. Marie-luce, P. Bliman, D. Di-penta, and M. Sorine, Control-Oriented Modeling of a LNT-SCR Diesel After-Treatment Architecture, SAE International Journal of Engines, vol.4, issue.1, pp.1764-1775, 2011.
DOI : 10.4271/2011-01-1307
URL : https://hal.archives-ouvertes.fr/hal-00655043

K. Rieif and R. Unbehauen, The extended Kalman filter as an exponential observer for nonlinear systems, IEEE Transactions on Signal Processing, vol.47, issue.8, pp.2324-2328, 1999.
DOI : 10.1109/78.774779

G. A. Einicke and L. B. White, Robust extended Kalman filtering, IEEE Transactions on Signal Processing, vol.47, issue.9, pp.2596-2599, 1999.
DOI : 10.1109/78.782219

J. R. Theis, M. Dearth, and R. Mccabe, LNT+SCR Catalyst Systems Optimized for Nox Conversion on Diesel Applications. SAE Technical Paper, pp.2011-2012, 2011.

L. Xu, R. Mccabe, P. Tennison, and H. W. Jen, Laboratory and Vehicle Demonstration of ???2nd-Generation??? LNT + in-situ SCR Diesel Emission Control Systems, SAE International Journal of Engines, vol.4, issue.1, pp.158-174, 2011.
DOI : 10.4271/2011-01-0308

R. E. Kalman, On the general theory of control systems, Proc. 1st IFAC Congress, 1960.
DOI : 10.1109/TAC.1959.1104873

R. E. Kalman, Mathematical Description of Linear Dynamical Systems, Journal of the Society for Industrial and Applied Mathematics Series A Control, vol.1, issue.2, pp.152-192, 1963.
DOI : 10.1137/0301010

P. V. Kokotovi´ckokotovi´c, Applications of singular perturbation techniques to control problems, SIAM, vol.26, issue.4, 1984.

A. Schuler, M. Votsmeier, P. Kiwic, J. Gieshoff, W. Hautpmann et al., NH 3 -SCR on Fe zeolite catalysts -From model setup to NH 3 dosing, Chemical Engineering Journal, pp.333-340, 2009.
DOI : 10.1016/j.cej.2009.02.037

N. Kato, K. Nakagaki, and N. Ina, Thick Film Z r O 2 NO x Sensor, SAE Technical Paper Series, 1996.

N. Kato, H. Kurachi, and Y. Hamada, Thick Film Z r O 2 NO x Sensor for the Measurement of Low NO x Concentration, SAE Technical Paper Series, 1998.

L. Cummaranatunge, S. S. Mulla, A. Yezerets, N. W. Currier, W. N. Delgass et al., Ammonia is a Hydrogen Carrier in the Regeneration of Pt, Journal of catalysis, issue.2, 2006.

D. Kondepudi and I. Prigogine, MODERN THERMODYNAMICS From Heat Engines to Dissipative Structures, 1998.

R. B. Banks, Growth and diffusion phenomena -Mathematical frameworks and applications, Texts in applied mathematics, 1994.

J. C. Wurzenberg and R. Wanker, Multi-Scale SCR Modeling, 1D Kinetic Analysis and 3D System Simulation. SAE Technical paper series, 2005.

V. Thomée, Galerkin finite elements method for parabolic problems, Lecture Notes in Mathematics, vol.25, 1984.
DOI : 10.1007/978-3-662-03359-3