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BooK (top)

S. Ganesan & L. Tobiska : Finite Elements: Theory and Algorithms. Cambridge University Press, 2017, ISBN: 9781108415705.

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Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.


   Indian Edition (available at Amazon)   International Edition


Journal Articles (top)

S. Srivastava, S. Ganesan: A stabilized local projection finite element approximation for computations of Oldroyd-B viscoelastic fluid flows. Int J Adv Eng Sci Appl Math, (2022)
S Ganesan, D Subramani, T Anandh, D Ghose, GR Babu: Ensemble forecast of COVID-19 in Karnataka for vulnerability assessment and policy interventions. (2021)  medRxiv
D Garg, S. Ganesan: An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems. (2021)  Applied Numerical Mathematics (Available online)
SM Joshi, T Anandh, B Teja, S Ganesan: On the choice of hyper-parameters of artificial neural networks for stabilized finite element schemes. (2021)  Int J Adv Eng Sci Appl Math (Available online)
S. Ganesan, D. Subramani: Spatio-temporal predictive modeling framework for infectious disease spread. (2021)  Nature Scientific Reports 11, 6741 (2021)
D. Garg, S. Ganesan: Generalized local projection stabilized nonconforming finite element methods for Darcy equations. Numerical Algorithms, (2021)  (Available online)
S. Ganesan, M. Singh: Error Analysis of the Operator-Splitting Finite Element Method for the Radiative Transfer Equation. (2021)   Journal of Scientific Computing. (submitted)
B. Pal, S. Ganesan: An a priori error analysis for a projection based variational multiscale finite element method for Oseen problems in a time-dependent domain. Comput. Math. with Appl., (2021), 82, 130-147  
D. Garg, S. Ganesan: Generalized local projection stabilized finite element method for advection-reaction problems. Journal of Applied Mathematics and Physics (ZAMP) (submitted)
S. Ganesan, M. Shah: SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods. arXiv, (2020)   arXiv:2007.00056
J. Venkatesan, S. Ganesan: Finite element computations of viscoelastic two-phase flows using Local Projection Stabilization. Int. J. Numer. Meth. Fluids, (2020)  92(8), 825-854
S. Srivastava, S. Ganesan: Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains. BIT Numerical Mathematics,(2019) 60, 481–507
J. Venkatesan, A. Padmanabhan, S. Ganesan: Simulation of viscoelastic two-phase flows with insoluble surfactants. Journal of Non-Newtonian Fluid Mechanics, (2019) 267, 61-77
J. Venkatesan, S. Ganesan: Computational modeling of impinging viscoelastic droplets. Journal of Non-Newtonian Fluid Mechanics, (2019) 263, 42-60
S. Srivastava, S. Ganesan: On the temporal discretizations of convection dominated convection-diffusion equations in time-dependent domain. Pro Mathematica, (2018) 30, 99-137
J. Venkatesan, S. Ganesan: A three-field local projection stabilized formulation for computations of Oldroyd-B viscoelastic fluid flows. Journal of Non-Newtonian Fluid Mechanics, (2017) 247, 90-106
U. Wilbrandt, C. Bartsch, N. Ahmed, N. Alia, F. Anker, L. Blank, A. Caiazzo, S. Ganesan, S. Giere, G. Matthies, R. Meesala, A. Shamim, J. Venkatesan, V. John: ParMoon - a modernized program package based on mapped finite elements. Computers and Mathematics with Applications, (2017)   74, 74-88
S. Ganesan, S.Srivastava: ALE-SUPG finite element method for convection-diffusion problems in time-dependent domains: Conservative form. Appl. Math. Comp., (2017)  303, 128-145
S. Ganesan, S. Lingeshwaran: Galerkin finite element method for cancer invasion mathematical model. Computers and Mathematics with Applications (2017)   73, 2603-2617
S. Ganesan, S. Lingeshwaran: A biophysical model of tumor invasion. Communications in Nonlinear Science and Numerical Simulation, (2017)   46, 135-152
P. Satish kumar, S. Ganesan: Numerical simulation of nanocrystal synthesis in a microfluidic reactor. Computers and Chemical Engineering, (2017)  96, 128 - 138
B. Pal, S. Ganesan: Projection based variational multiscale method for incompressible Navier--Stokes equations in time-dependent domains. Int. J. Numer. Meth. Fluids, (2017)   84, 19-40
S. Ganesan, V. John, G. Matthies, R. Meesala, S. Abdus, U. Wilbrandt: An object oriented parallel finite element scheme for computations of PDEs: Design and implementation. IEEE 23rd International Conference on High Performance Computing Workshops (HiPCW) (2016),   DOI 10.1109/HiPCW.2016.023  
J. Venkatesan, S. Rajasekaran, A. Das, S. Ganesan: Effects of temperature-dependent contact angle on the flow dynamics of an impinging droplet on a hot solid substrate. Int. J. Heat and Fluid Flow, (2016)   62, 282-298
S.Mohapatra, S. Ganesan: A Non-Conforming Least Squares Spectral Element Formulation for Oseen Equations with Applications to Navier-Stokes Equations. Numerical Functional Analysis and Optimization, (2016),  37, 1295 - 1311
J. Venkatesan, S. Ganesan: On the Navier-slip boundary condition for computations of impinging droplets. IEEE 22nd International Conference on High Performance Computing Workshops (HiPCW) (2015),   2-11, DOI 10.1109/HiPCW.2015.10  
S. Ganesan: Simulations of impinging droplets with surfactant-dependent dynamic contact angle. J. Comput. Phys., (2015), 301, 178 - 200  
B. Pal, S. Ganesan: A finite element variational multiscale method for computations of turbulent flow over an aerofoil. Int. J. Adv. Engg. Sci. Appl. Math., (2015), 7, 14 - 24  
S. Ganesan, J. Venkatesan, S. Rajasekaran: Modeling of the non-isothermal liquid droplet impact on a heated solid substrate with heterogeneous wettability. Int. J. Heat Mass Transfer, (2015), 88, 55 - 72  
F. Ankera, S. Ganesan, V. John, E. Schmeyer: A comparative study of a direct discretization and an operator-splitting solver for population balance systems. Computers and Chemical Engineering, (2015), 75, 95 - 104  
S. Ganesan, S. Rajasekaran, L. Tobiska: Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate. Int. J. Heat Mass Transfer, (2014), 78, 670 - 687  
S. Ganesan: On the dynamic contact angle in simulation of impinging droplets with sharp interface methods. Microfluidics and Nanofluidics, Springer, (2013), 14, 615-625 
S. Ganesan, P. K. Yalavarthy: Modeling of Terahertz Heating Effects in Realistic Tissues. IEEE Journal of Selected Topics in Quantum Electronics (Issue on current trends in terahertz photonics and applications), 2013 19(1), pp.8400908 
S. Ganesan, L. Tobiska: Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems. Appl. Math. Comp., (2013)  219, 6182 - 6196
S. Ganesan: An operator-splitting Galerkin/SUPG finite element method for population balance equations: Stability and convergence. ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), (2012) 46,46, 1447-1465  
S. Ganesan, L. Tobiska: Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants. J. Comput. Phys., (2012) 231 (9), 3685-3702 
M. Krasnyk, M. Mangold, S. Ganesan, L. Tobiska: Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition. Chem. Eng. Sci., (2012) 70, 77-86 
S. Ganesan, L. Tobiska: An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems. Chem. Eng. Sci., (2012)  69 (1), 59-68
U. Kornek, F. Müller, K. Harth, A. Hahn, S. Ganesan, L. Tobiska, R. Stannarius: Oscillations of soap bubbles. New J. Phys., (2010) 12, 073031 
S. Ganesan, L. Tobiska: Stabilization by local projection for convection-diffusion and incompressible flow problems. J. Sci. Comput., (2010)  43 (3), 326-342
S. Ganesan, L. Tobiska: A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants. J. Comput. Phys., (2009) 228 (8), 2859-2873 
S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, L. Tobiska: Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Meth. Fluids, (2009)   60, 1259-1288
S. Ganesan, L. Tobiska: Modelling and simulation of moving contact line problems with wetting effects. Comput. Visual. Sci., (2009)  12, 329-336
S. Ganesan, G. Matthies, L. Tobiska: Local projection stabilization of equal order interpolation applied to the Stokes problem. Math. of Comput., (2008)  77, 2039-2060
S. Ganesan, L. Tobiska: An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flows. Int. J. Numer. Meth. Fluids, (2008)   57(2), 119 - 138
S. Ganesan, G. Matthies, L. Tobiska: On spurious velocities in flow problems with interfaces. Comput. Methods Appl. Mech. Engrg., (2007)  196, 1193 - 1202
S. Ganesan, V. John: Pressure separation - a technique for improving the velocity error in finite element discretisations of the Navier-Stokes equations. Appl. Math. Comp., (2005)  165, 275 - 290


Book Chapters (top)

S. Ganesan, A. Hahn, K. Simon, L. Tobiska: Finite Element Computations for Dynamic Liquid-Fluid Interfaces. In: M. T. Rahni, M. Karbaschi and R. Miller, editors, Computational Methods for Complex Liquid-Fluid Interfaces, CRC Press, Taylor and Francis Group, (2015) Ch.16, Pages: 331--351, ISBN: 9781498722087 (online) 

S. Ganesan, B. Pal, S.Srivastava: Simulation of two-phase flows with surfactants. In: N. K. Gupta, A. V. Manzhirov, and R. Velmurugan, editor, Topical problems in theoretical and applied mechanics, Elite Publishing House Pvt. Ltd., (2013) Pages: 418 - 425, ISBN: 978-81-88901-55-5 

S. Ganesan, Bhanu Teja: A multi-level finite element discretization for efficient solution of multidimensional population balance system. In: S. Sundar, editor, Advances in PDE Modeling and Computation, Ane Books Pvt. Ltd., (2013), Pages: 105 - 118 (online) 

S. Ganesan, S. Rajasekaran, L. Tobiska: An ALE-based finite element method for the simulation of an impinging droplet on a hot surface. In: S. Sundar, editor, Advances in PDE Modeling and Computation, Ane Books Pvt. Ltd., (2013), Pages: 35 - 53 (online) 

S. Ganesan, L. Tobiska: Finite Element Simulation of an Impinging Liquid Droplet. In: Albrecht Bertram and Jürgen Tomas, editor, Micro-Macro- Interactions In Structured Media and Particle Systems, Springer, (2008) (online) 

S. Ganesan, L. Tobiska: A Finite Element Method for the Simulation of a Liquid Droplet Impinging on a Solid Surface. In: Palle Jorgensen, Xiaoping Shen, Chi-Wang Shu and Ningning Yan, editor, RECENT ADVANCES IN COMPUTATIONAL SCIENCES, World Scientific, (2008) (online) 



Conference Contributions (top)

S. Ganesan, A. Hahn, K. Held, L. Tobiska: An accurate numerical method for computation of two-phase flows with surfactants. ECCOMAS 2012, J. Eberhardsteiner et. al. (eds.), Vienna, Austria., Sept 10-14, CD-ROM, ISBN: 978-3-9502481-9-7 

M. Krasnyk, M. Mangold, S. Ganesan, L. Tobiska: Reduction of a Crystallizer Model by Proper Orthogonal Decomposition.   Proceedings of 4th International Conference on Population Balance Modelling, Berlin, 301--317, 2010

L. Tobiska, S. Ganesan: Finite element methods for interface flows with surfactants.   Mathematisches Forschungsinstitut Oberwolfach, Workshop: New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries, 2010

S. Ganesan, L. Tobiska: Non-Isothermal Spreading of a Liquid Droplet with Dynamic Contact Angles on a Horizontal Surface.   Proceedings of International Conference on Multiphase Flow, Leipzig, Germany, 2007 (publication)

S. Ganesan, L. Tobiska: On the Influence of Finite Element Discretisations on Spurious Velocities in Two-Phase Flows.   Proceedings of International Conference on Multiphase Flow, Leipzig, Germany, 2007 (publication)

S. Ganesan, L. Tobiska: Computations of flows with interfaces using arbitrary Lagrangian Eulerian method. Proceedings of ECCOMAS CFD 2006, Egmond aan Zee, The Netherlands, ISBN 90-9020970-0, 2006(publication)

S. Ganesan, L. Tobiska: Finite element simulation of a droplet impinging a horizontal surface.   Proceedings of Algoritmy 2005  , Podbanske, Slovakia, ISBN 80-227-2192-1, 1--11. 2005

S. Ganesan, L. Tobiska: Droplet Deformation with Navier Slip and Free Boundaries by Finite Elements.   Mini-Workshop: Interface Problems in Computational Fluid Dynamics, Mathematisches Forschungsinstitut Oberwolfach  , Organized by: Noel J. Walkington, Lutz Tobiska and Eberhard Baensch, European Mathematical Society, 2(1), 474--476, 2005