Education

• B.Sc : Vardhman College Bijnor  (M.J.P. Rohilkhand University, Bareilly), 1998.
• M.Sc : Vardhman College Bijnor (M.J.P. Rohilkhand University, Bareilly), 2000.
• Ph.D : IIT Bombay (2008).

Course Offered

Calculus, Differential equations, Linear Algebra ,  complex Analysis, Functional Analysis, Numerical Analysis and  Partial differential equations.

Experience

• Research Associate in the Department of Mathematics at IIT Bombay from  April  2008 to  August 2008
• Sep 2008 to April 2011, Assistant professor, BITS, Pilnai-K.K.  Birla Goa Campus, Goa.

Research Work / Area

• Computational Partial Differential Equations
• Finite Volume Element Methods
• Finite Element Methods
• Discontinuous Galerkin  Methods.

Refereed International Journals:

1. Sarvesh Kumar, Neela Nataraj and  Amiya K. Pani:  “Finite Volume Element Method for Second Order Hyperbolic Equations”. International Journal of  Numerical Analysis and Modeling, Vol. 5 (2008), 132-151.
2. Sarvesh Kumar, Neela Nataraj and Amiya K. Pani: “Discontinuous Finite Volume Element Methods for Second Order Linear Elliptic Problems”.  Numerical Methods for Partial Differential Equations,  Vol.25 (2009), 1402-1424.
3. Sarvesh Kumar: “A  Mixed and Discontinuous Finite Volume Element Method for Incompressible Miscible Displacement in Porous Media”,  Numerical Methods for Partial Differential Equations. Vol. 28(2012), 1351-1381.
4. Sarvesh Kumar: “On the approximations incompressible miscible displacement problems in porous media by mixed and standard finite volume element methods”, International Journal of Modeling, Simulation and Scientific Computing, 4(3), ID 1350013, 2013.
5. Sarvesh Kumar and Sangita Yadav :Modified methods of characteristics combined finite volume element methods for incompressible miscible displacement problems in porous media.” International Journal of Partial Differential Equations, ID 245086, 16 pages,  2014.
6. Raimund Burger, Sarvesh Kumar and Ricardo Ruiz-Baier: Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation, Journal of Computational Physics, 299 (2015), 446-471.
7. Sarvesh Kumar and Ricardo Ruiz -Baier: Equal-order discontinuous finite   volume elements for the Stokes problem, Journal of Scientific Computing, 65 (2015), 956-978.
8. Ruchi Sandilya and Sarvesh Kumar: Convergence analysis of discontinuous finite volume method for elliptic control problems, International Journal of Computational Methods, 13 (2016), 1640012 (20 pages) .
9. Ruchi Sandilya and Sarvesh Kumar: On discontinuous finite volume approximations for semilinear parabolic optimal control problems, International Journal of Numerical Analysis and Modeling, Vol 14(2016), 545-568 .
10. Raimund Burger, Sarvesh Kumar, Sudarshan Kumar K and Ricardo Ruiz-Baier: Discontinuous approximation of viscous two-phase flow in heterogeneous porous media, Journal of Computational Physics, 321 (2016), 126-150.
11. Ruchi Sandilya and Sarvesh Kumar: Convergence of discontinuous finite volume discretizations for a semilinear hyperbolic optimal control problem, International Journal of Numerical Analysis and Modeling,Vol. 13 (2016), 926-950
12. Dibyendu Adak, E. Natarajan and Sarvesh Kumar: A new nonconforming finite element method for convection dominated diffusion -reaction equations, International Journal of Advances in Engineering Sciences and Applied Mathematics Vol 8 (2016), 274-283.
13. Ruchi Sandilya and Sarvesh Kumar: Discontinuous interpolated finite volume approximations for semi-linear elliptic control problems, Numerical Methods for Partial Differential Equations Vol 33 (2017), 2090-2113
14. Dibyendu Adak, E. Natarajan and Sarvesh Kumar: Virtual Element Methods for semilinear hyperbolic  problems on polygonal meshes, International Journal of Computer Mathematics, Vol 96 (2019),971–991
15. Dibyendu Adak, E. Natarajan and Sarvesh Kumar: Convergence analysis of Virtual Element Methods for semilinear parabolic problems on polygonal meshes,  Numerical Methods for Partial Differential Equations, Vol. 35 (2019), 222-245
16. Sarvesh Kumar, Ricardo-Ruiz Baier and Ruchi Sandilya: Error Bounds for Discontinuous Finite Volume Discretisations of Brinkman Optimal Control Problems, Journal of Scientific Computing, Vol 78 (2019), 64-93
17. Sarvesh Kumar, Ricardo-Ruiz Baier and Ruchi Sandilya: Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media, Computers and Mathematics with Applications, Vol 76 (2018), 923–937.
18. Sarvesh Kumar, Ricardo Oyarxua, Ricardo-Ruiz Baier and Ruchi Sandilya: Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity, M2AN:ESIAM, Vol 54 (2020), 273 - 299.
19. L.M. De Oliveira Vilaca, B. Gomez-Vargas, S. Kumar, R. Ruiz-Baier, and N. Verma, Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue. Appl. Math. Model., 84 (2020), 425-446.

20. Raimund  Burger, Sarvesh  Kumar, David Mora, Ricardo Ruiz-Baier, and Nitesh  Verma, Virtual element methods for the three-field formulation of time-dependent linear poroelasticity,   Adv. Comput. Math.  47  (2) (2021) ; https://doi.org/10.1007/s10444-020-09826-7

21. N. Verma, B. Gomez-Vargas, L.M. De Oliveira Vilaca, S. Kumar, and R. Ruiz-Baier, Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media. Applic. Anal., (2021)  https://doi.org/10.1080/00036811.2021.1877677.

22.  N. Verma and S. Kumar, Lowest order virtual element approximations for transient Stokes problem on polygonal meshes. Calcolo 58, 48 (2021). https://doi.org/10.1007/s10092-021-00440-7. 

23. J. Tushar, A. Kumar & S. Kumar. Approximations of Quasi-Linear Elliptic Optimal Control Problems on Polygonal Meshes Under Variational and Virtual Discretizations. Int. J. Appl. Comput. Math 8, 24 (2022). https://doi.org/10.1007/s40819-021-01215-y

24. J. Tushar, A. Kumar & S. Kumar, Variational and virtual discretizations of optimal control problems governed by diffusion problems", Applied Mathematics and Optimization, 2 (2022). https://doi.org/10.1007/s00245-022-09872-1.

25. Nitesh Verma and Sarvesh Kumar, Virtual element approximations for two species model of the Advection-diffusion-reaction in a poroelastic media, Mathematical Modelling and Analysis, Volume 27, Issue 4, 668–690, 2022, https://doi.org/10.3846/mma.2022.15542

26. Nitesh  Verma and Sarvesh  Kumar, Virtual element approximations for non-stationary Navier-Stokes equations on polygonal meshes, Journal of  Applied Analysis and Computation, Volume 13, Number 3, June 2023, 1155–1177, DOI:10.11948/20210381

27. Jai Tushar, Anil Kumar and Sarvesh Kumar, Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges,  Computers and Mathematics with Applications,  122 (2022) 61–75, https://doi.org/10.1016/j.camwa.2022.07.016

28. Jai Tushar, Anil Kumar and Sarvesh Kumar, Mixed virtual element methods for optimal control of Darcy flow, Computers and Mathematics with Applications,  140 (2023) 134–153, https://doi.org/10.1016/j.camwa.2023.04.022

29.  Sangita Yadav, Meghna Suthar and Sarvesh Kumar, A conforming Virtual Element Method for Parabolic Integro-Differential Equations, Computational methods in Applied Mathematics, https://doi.org/10.1515/cmam-2023-0061

30. Sarvesh Kumar, David Mora, Ricardo Ruiz-Baier and Nitesh Verma, Numerical Solution of the Biot/Elasticity Interface Problem Using Virtual Element Methods, Journal of Scientific Computing (2024) 98:53 https://doi.org/10.1007/s10915-023-02444-7

31. angita Yadav, Meghna Suthar and Sarvesh Kumar :Mixed Virtual Element Method for Integro-Differential Equations of Parabolic type, Journal of Applied Mathematics and Computing, available online, DOI 10.1007/s12190-024-02066-8

Proceedings of International Conferences:

1. Sarvesh Kumar, Neela Nataraj and  Amiya K. Pani : “Finite Volume Element Method for the Incompressible Miscible Displacement Problems in Porous Media”  Proc. Appl. Math. Mech. (PAMM) vol. 7, pp. 2020015-2020016, 2007.
2. Sarvesh Kumar: Discontinuous finite volume element methods and its applications in miscible displacement problems, appeared in the proceedings of SCTEMM 2013, held at Russia, July 08-13, 2013..
3. Sarvesh Kumar: Finite volume approximations for incompressible miscible displacement problems in porous media with modified methods of characteristics”, LNCS, pp. 379-386, 2013
4. Ruchi Sandilya and Sarvesh Kumar: Discontinuous finite volume element methods for elliptic optimal control problem, appeared in the Proceedings of ICCM 2014, held at Cambridge, England, July 28-30, 2014.2.
5. Ruchi Sandilya and Sarvesh Kumar: Discontinuous finite volume methods for parabolic optimal control problems", Proceedings of International Conference on Mathematics, November 26-28, 2015, University of Kerala. Mathematical Sciences International Research Journal, Vol. 4(2), 15-22, 2015.
6. Raimund Burger, Sarvesh Kumar, Sudarshan Kumar K and Ricardo Ruiz-Baier: A discontinuous method for oil-water flow in heterogeneous porous media, Proc. Appl. Math. Mech. (PAMM) vol. 16, pp. 763-764, 2016. .
7. S. Kumar, R. Ruiz Baier, and R. Sandilya : Discontinuous finite volume element methods for the optimal control of Brinkman equations. In C. Cancès and P. Omnes, editors, Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, volume 200 of Springer Proc. Math. Stat., pages 307–315. Springer International Publishing, 2017.
8. Ruchi Sandilya, Raju. K. George, Sarvesh Kumar, Trajectory controllability of semilinear parabolic system, Journal of analysis, DOI 10.1007/s41478-017-0048-3, Proceedings of ICMAA.
9. Jai Tushar, Anil Kumar and Sarvesh Kumar: Virtual Element Methods for Optimal Control Problems Governed by Elliptic Interface Problems. In: Sharma, R.K., Pareschi, L., Atangana, A., Sahoo, B., Kukreja, V.K. (eds) Frontiers in Industrial and Applied Mathematics. FIAM 2021. Springer Proceedings in Mathematics and Statistics, vol 410. Springer, Singapore. (2023) https://doi.org/10.1007/978-981-19- 7272-0_36

1. A session " Numerical solution of nonlinear system" in short term course on "Dynamical Systems and Chaos theory" organised by the Department of Mathematics, College of Engineering Trivandrum sheduled for the 4th to 6th of January 2016.
2. Two lectures on “ linear algebra” in 3-day FDP on “ Recent trends in Signal Processing” , 01-03, March 2017, College of Engineering, Cherthala, Kerala
3. Ten lectures in lecture series on " Numerical techniques and programming in MATLAB, at Purvanchal University, July 22-28, 2016.
4. Three lectures in "Workshop on high performance scientific computing" IISER Trivandrum, 09-10 June, 2016.
5. Six lectures on "Numerical solution of ODEs" in NPDE-TCA's under graduate programme, IIST Trivandrum, May 18-June 07, 2016.
6. Three lectures in "Workshop on high performance scientific computing" IISER Trivandrum, 09-10 June.
7. Four lectures in YTN-2016, IIST, during May 24-June 06, 2016.
8. Six lectures in "Computational Techniques for differential equations" SVNIT Surat, 02-06 May, 2016.
9. Two lectures in faculty training programme on "Differential Equations and its applications"   College of Engineering Karunagapally, Kerala, Feb. 25, 2016.
10. Delivered three lectures in faculty development programme on "Mathematical Techniques in Engineering Research” at RIT Kottayam, Kerala December 11, 2015..
11. Delivered five lectures in a workshop on "Numerical Computation using MATLAB " held at Purvanchal University, Jaunpur U.P, November 26-30, 2015 .
12. Delivered two lectures in faculty training programme at College of Engineering Karunagapally, Kerala, October 28, 2015.
13. Two talks at VSSC in a 2 Days training programme on “CFD in Propulsion", August 6-7, 2015.
14. Delivered two lectures on finite element methods for control problems in the workshop on “Computational methods for control problems held at Mar Ivanios College Trivandrum, March 16-21, 2015.
15. Delivered three lectures on Linear Algebra and Applications in “Young talent nurture programme" organized by IIST Trivandrum, 28th May to 8th June, 2013.
16. Given 2 lectures on Theoretical Finite Element Methods in Intensive Workshop on "Scienctific Computation" during 21 July 2009 to 25 July, 2009, BITS Goa.

1. VSSC project:  Project accepted with VSSC ( Vikaram Sarabhai Space Center)  SMSD Team in developing modules for FEAST Software (Finite element analysis of structures), this project is jointly written with Dr. E. Natarajan, Assistant Professor, Department of Mathematics, IIST Trivandrum.

• Project Title:  Algebraic Multi-grid methods (AMG) for solving  sparse linear system
• Grant:  Approx.  5 lacs
• Duration: 1 and ½ year.
• Date of approval: April 13, 2016

2.   IIST  Project: An IIST research proposal which was submitted to IIST Trivandrum jointly written with Dr. Deepak Mishra (Department of Avionics, IIST Trivandrum):

• Project title:Development and Analysis of Image Fusion Techniques for Satellite Images.
• Duration:  2 year.
• Grant:  6 lacs
• Date of acceptance:  28/10/2015

• Advanced level workshop on  "computational methods for control problems" March 16-21, 2015, Jointly organized by IIST Trivandrum and Mar Ivanios college Trivandrum and held at Mar Ivanios college Trivandrum
• International workshop on " Adaptive finite element methods" March 16-25, 2012, Indian Institute of Space Science and Technology Trivandrum, India
• International workshop on "Advances in Computational partial differential equations", 7 feb-5 March, 2011,  BITS-Pilani, Goa Campus.
• Intensive Workshop on "Scienctific Computation" during  21 July 2009 to 25 July, 2009 for research scholars and faculty members of BITS Pilani Goa Campus.

1. Ruchi sandilya, Thesis title: Discontinuous finite volume methods for optimal control problems ( Degree Awarded)

 2. Nitesh Verma, Theis title: Virtual element approximations for transient fluid flow problems on polygonal meshes ( Ongoing)

3. Utkarsh Rajput , Thesis title: Virtual element methods for nonlinear problems  (Ongoing)

1. DST-SERB  MATRICs Project (MTR/2019/000519): 

• Title: Discontinuous virtual element approximation for non-stationary fluid flow problems (started in March 2020).  
• Amount: 660000 (in INR)
• Duration : 3 years (2020 to 2023)

3.   DST-SERB CRG Project (CRG/2019/003863 ) (Co-PI)

• Title: Numerical Approximation  of Optimal Control Problems Using Virtual Element Method (started in Janurary 2020) 
• Amount: 1907400 (in INR)
• Duration: 3 years (March 2020 to March 2023)