Finite Element Methods for PDEs(2023) | National Centre for Mathematics

Convener(s)


Name:	Prof. Neela Nataraj	Dr. Nagaiah Chamakuri
Mailing Address:	Institute Chair Professor, Department of Mathematics, Indian Institute of Technology Bombay Powai, Mumbai, India - 400076	Assistant Professor School of Mathematics IISER Thiruvananthapuram, Kerala, 695551, India.
Email:	neela at math.iitb.ac.in	nagaiah.chamakuri at iisertvm.ac.in

Partial Differential Equations(PDEs) play an important role in science and engineering applications, such as the propagation of heat or sound, fluid flow, finite elasticity, electrodynamics, cancer modeling, etc. In general, the solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary and initial conditions, and nonlinearities. Even if we know the theoretical existence and uniqueness of the solution, obtaining analytical solutions may not be possible. The only way to get approximate solutions is by using numerical techniques. The finite element (FE) and discontinuous Galerkin (dG) method provide a formalism for generating discrete algorithms for approximating the solutions of differential equations. The finite element method (FEM) has a very strong foundation in the theory of functional analysis, and this gives us access to powerful tools when analyzing the error of the approximate solution. The variational approach also gives a solid mathematical foundation and make the error analysis more systematic. Generally speaking, the finite element method is the method of choice in all types of analysis for elliptic equations in complex domains. This workshop offers an introduction to some important numerical methods for linear and non-linear partial differential equations, and various numerical discretization techniques for their solution, namely finite element methods (FEM), and discontinuous Galerkin methods (DGM). It starts with a brief introduction to Sobolev spaces and elliptic scalar problems and continues with an explanation of finite element spaces and estimates for the interpolation error. This workshop aims to show how this abstraction can be used not only to analyze the stability and convergence of FE or dG methods, but also to understand the realization of the abstraction into concrete computer code using the numerical softwares.

Click here to download poster

Dates:

Monday, September 11, 2023 - 19:00 to Saturday, September 16, 2023 - 19:00

Venue:

IISER

Venue Address:

School of Mathematics
IISER Thiruvananthapuram,
Kerala, 695551, India.

Venue State:

Kerala

Venue City:

Thiruvananthapuram

PIN:

695551

Chrono Order:

430

Syllabus:

Syllabus:

Name of the Speaker with affiliation	No.of Lectures	Detailed Syllabus
Sheetal Dharmatti, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram	3 lectures of 1 and half hours each	Overview of Weak derivatives, Sobolev spaces and embeddings, Poincare inequality, Dual spaces, trace spaces.
S. Kesavan, Professor, The Institute of Mathe- matical Sciences, Chennai	4 lectures of 1 and half hours each	Some abstract variational problems (Stampac- chia, Lax Milgram, Babuska Brezzi), Examples of elliptic problems, Regularity of weak solu- tions.
Neela Nataraj Profes- sor, Department of Mathe- matics, Indian Institute of Technology Bombay	4 lectures of 1 and half hours each	Conforming, Mixed FEM, dGFEM for second order elliptic equations, Interpolation, and ap- proximation, Error estimates.
Nagaiah Chamakuri, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram	4 lectures of 1 and half hours each	Discretization of Poisson’s problem. Aspects of efficient implementation: Mesh handling and data structure, Numerical integration, Sparse matrix storage, Local and global assembly of system matrices and load vectors, including vari- ous boundary conditions, and solving the assem- bled system.
Asha K Dond, As- sistant Professor, School of Mathematics, IISER Thiruvananthapuram	2 lectures of 1 and half hours each	Stokes Problem- Mixed FEM formulation, Error estimates. Aspects of efficient implementation.

Time Table:

Time/Day	11-09-2022	12-09-2022	13-09-2022	14-09-2022	15-09-2022	16-09-2022
09:00-10:30	SD	SK	SK	NN	NN	NN
10:30-11:00	Tea	Tea	Tea	Tea	Tea	Tea
11:00-12:30	SK	SD	NC	NC	AD	AD
12:30-14:00	Lunch	Lunch	Lunch	Lunch	Lunch	Lunch
14:00-15:30	SD	SK	NC	NN	NC	NC
15:30-16:00	Tea	Tea	Tea	Tea	Tea	Tea
16:00-17:00	T(AK+NR)	T(NC+NR)		T(AD+AVS)	T(AD+RK)	T(NC+NR)

Note: T(XYZ): Discussion class/Lab session by XYZ. Some aspects of implementation in MATLAB will be integrated in the lectures. Participants will be provided lab facilities outside of the lecture hours.

Full forms for the abbreviations of speakers and tutors:

• Speakers
– SD: Sheetal Dharmatti (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)
– AD: Asha K Dond (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)
– NC: Nagaiah Chamakuri (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)
– SK: S. Kesavan (Professor, The Institute of Mathematical Sciences, Chennai)
– NN: Neela Nataraj (Professor, Department of Mathematics, IIT Bombay, Mumbai)

• Tutors
– RK: Rakesh Kumar (Postdoc, School of Mathaematics, IISER Thiruvananthapuram)
– NR: Nishant Ranwan (PhD, School of Mathaematics, IISER Thiruvananthapuram)
– AVS: Aswin V.S (Assistant Professor, Amrita Vishwa Vidyapeetham, Coimbatore)

• References
– S. Kesavan, Topics in Functional Analysis and Applications, New Age International Private Limited, 2015.
– E. Süli & David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003.
– S.C. Brenner & L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer, 2nd edition, 2002.
– C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method. CUP, 1990.
– J.C. Strikwerda, Finite difference schemes and Partial differential equations, Wordsworth and Brooks, 1989.
– H. Elman, D. Silvester & A. Wathen, Finite Elements and Fast Iterative Solvers. Second edition, 2014.
– Sashikumaar Ganesan & Lutz Tobiska, Finite elements: Theory and Algorithms, Cambridge University Press, 2017.
– P.G. Ciarlet, The finite element method for elliptic problems, North-Holland, 1978.
– D. Di Pietro and A. Ern. Mathematical Aspects of Discontinuous Galerkin Methods. Mathématiques et Applications. Springer Berlin Heidelberg, 2011.

Selected Applicants:

Sr.n	SID	Full Name	Gender	Affiliation	Position in College/ University	University/ Institute M.Sc. /M.A.	Year of Passing M.Sc. /M.A	Ph.D. Deg. Date
1	48462	Ms. Heena	Female	National Institute of Technology Warangal	PhD	Banaras Hindu University	2019
2	48625	Mr. Achyuta Ranjan Dutta Mohapatra	Male	IIT Guwahati	PhD Student	Utkal University	2020
3	48626	Ms Manisha Vasantrao Kolhe	Female	Institute of Chemical Technology, Indian Oil Campus, Bhubaneswar.	Ph.D. Student	M.Sc., Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra.	2018
4	48727	Ms Aasna Chauhan	Female	Department of Mathematics, University of Delhi, Delhi	Research scholar	Rajasthan University	2018
5	48781	Mr Bamadev Sahoo	Male	SOA UNIVERSITY	PHD	Percentage	2013
6	48819	Ms. Shallu Shallu	Female	The LNM institute of information technology Jaipur	PhD	Indian institute of technology Kharagpur	2021
7	49164	Mr Mukul Dwivedi	Male	IIT Jammu	PhD	IIT Guwahati	2020
8	49220	Ms. Kousalya R	Female	National Institute of Technology Tiruchirappalli	PhD Scholar	Central University of Tamilnadu	2021	23/08/2022
9	49230	Mr. Raghunath Bandha	Male	IIT Guwahati	PhD	IIT Kharagpur	2020
10	49251	Mr. Akash Panwar	Male	The LNM Institute of Information Technology	PhD Student	The LNM Institute of Information Technology	2021
11	49307	Mr. Gangadhara B	Male	IIT Tirupati	PhD student	Bengaluru university	2017
12	49374	Mr Ankit Pandey	Male	South Asian University	Ph.D.	Sout Asian University	2022
13	49447	Ms Sonia Jangra	Female	BML Munjal University Gurgaon Haryana	PhD Student	Maharshi Dayanand University Rohtak Haryana	2018
14	49449	Ms. Ramya K	Female	National Institute of Technology, Puducherry (NITPY)	Ph.D	CGPA	Pursuing Ph.D
15	49713	Mr. Navaneetha Krishnan M	Male	Central University of Tamil Nadu	PhD	PSG College of Arts and Science	2018
16	49781	Mr. Jayesh Bhardwaj	Male	The LNM Institute of Information Technology	PhD	Indian Institute of Technology, Ropar	2020
17	50115	Mr Rohit Sharma	Male	National institute of technology Hamirpur H.P	Phd	H.P.U	2018
18	50273	Mr Gokul Santhosh	Male	Indian Institute of Technology Palakkad	PhD Student	Indian Institute of Technology Palakkad	Appeared
19	50284	Mrs Hiba Mohamed	Female	Indian Institute of Technology Palakkad	Msc student	CGPA		Not workings
20	50349	Ms. Anjaly Anand	Female	NIT Calicut	PhD	NIT CALICUT	2014
21	50434	Mr. Shishu Pal Singh	Male	Rajiv Gandhi Institute of Petroleum Technology	PhD	Delhi University	2020
22	50479	Ms. Shreya Rajeshbhai Chauhan	Female	Institute of Infrastructure, Technology, Research And Management (IITRAM)	PhD Student	Sardar Patel University, Vallabh Vidyanagar, Gujarat	2020
23	50501	Ms. Raksha Devi	Female	Indian Institute of Technology, Roorkee Uttarakhand	PhD	University of Lucknow, Lucknow	2018
24	50502	Ms Aparna Bansal	Female	Indian Institute of Technology Roorkee, Roorkee	PhD	IIT Jodhpur, Mathematics	2020
25	50512	Mr. Ayush Agrawal	Male	Indian Institute of Technology Roorkee	Phd	Indian Institute of Technology Gandhinagar	2019
26	50650	Ms. Nithiya V	Female	Vellore Institute of Technology	PhD	Government Arts College (Autonomous), Coimbatore	2022
27	50743	Mr Subham Jangid	Male	National institute of technology, Warangal	Phd	CGPA	2020
28	50747	Mr. Shridhar Kumar	Male	INDIAN INSTITUTE OF TECHNOLOGY PATNA	PhD	Indian Institute of Technology Patna	2019
29	50883	Ms. Sweta Chakraborty	Female	Tezpur University	PhD	Cooch Behar Panchanan Barma University	2020
30	50903	Ms. Pooja Biswas	Female	Tezpur University	PhD	MSc	2021
31	50956	Mr. Ankit Kumar	Male	BITS Pilani, Pilani Campus	PhD	Indian Institute of Technology Roorkee	2020
32	50965	Mr Tarun Sharma	Male	Indian Institute of Space Science and Technology	PhD	Gurukul Kangri Vishwavidyalaya, Uttarakhand.	2015
33	50993	Ms. Rinki Rawat	Female	Indian Institute of Technology	PhD	University of Lucknow	2019
34	51050	Ms Aswini N K	Female	INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY	PhD	University of Calicut	2018
35	51079	Mr Deepak Kumar	Male	NIT Patna	Research Scholar	NIT Trichy	2021
36	51100	Ms. Alphonsa George	Female	IIT Palakkad	PhD	Mahatma Gandhi University	2020
37	51104	Mr Akshay Kumar	Male	Malaviya National Institute of Technology Jaipur	PhD	IIT Madras	2019
38	51110	Ms. Shivangi Joshi	Female	BITS Pilani Hyderabad Campus	Ph.D.	University of Hyderabad	2018
39	51115	Ms. Sandhya Mel	Female	Bits Pilani, Hyderabad Campus	PhD	M.Sc.	2019
40	51116	Ms. Shravani Nakidi	Female	BITS Pilani Hyderabad	PhD	NIT Warangal	2017
Local Participants
1	50748	Ms. Gopika P B	Female	IISER Thiruvananthapuram	PhD	National Institute of Technology Calicut	2020
2	50755	Mr Swapnil Vishwanath Kale	Male	IISER Thiruvananthapuram	Research Associate	Savitribai Phule Pune University Pune	2018
3	50760	Mr. Nishant Ranwan	Male	IISER Thiruvananthapuram	PhD	Indian Institute of Technology, Patna	2021
4	50805	Mr. Vivek Singh Yadav	Male	IISER Thiruvananthapuram	Research Associate	MNNIT Allahabad UP	2015
5	51011	Mr Ankur Upadhyay	Male	IISER Thiruvananthapuram	Phd	MSc	2022
6	51026	Mr. Siyad Rahman. M	Male	IISER Thiruvananthapuram	MSc Student	IISER Thiruvananthapuram	Appeared
7	51051	Ms Tooba M. Shaikh	Female	IISER Thiruvananthapuram	IPhD Student	Indian Institute of Science Education and Research,Thiruvananthapuram-Kerala.	2022
8	51063	Mr. Subham Nayak	Male	IISER Thiruvananthapuram	PhD	Pondicherry University	2019
9	51087	Mr Amogh Krishnamurthy	Male	IISER Thiruvananthapuram	PhD student	IISER Thiruvananthapuram	2022
Waiting List
1	48614	Ms. Sharmistha Rakshit	Female	Indian Institute of Information Technology Kalyani	Research Scholar	IIT(ISM) Dhanbad	2016
2	50631	Mr. Kathuroju Santhosh Kumar	Male	Defence Institute of Advanced Technology	PhD Student	Osmania University	2014
3	50649	Ms. Jeyashri K	Female	Vellore Institute of Technology, Chennai	PhD	Ayya Nadar Janaki Ammal College, Sivakasi.	2022
4	50124	Ms. Anamika Pandey	Female	IIT Kharagpur	Ph.D.	IIT Kharagpur	2019
5	48594	Mr. Jyotiranjan Nayak	Male	SRM University, AP	PhD	Sambalpur University, Burla	2020
6	48595	Mr Shafeequdheen P	Male	SRM university AP	PhD	Calicut university Department	2014
7	49714	Ms. Deeksha Tomer	Female	Indian Institute of Technology Bhubaneswar	PhD	University of Lucknow	2019
8	49759	Mr. Deepak Kumar	Male	University of Delhi	PhD	University of Delhi	2022
9	49946	Mr. Anandasrinivasan S	Male	National Institute of Technology Tiruchirappalli	PhD Research Scholar	Madurai Kamaraj University	2015
10	50285	Mr Kumar Rajeev Ranjan	Male	NIT Patna	Ph.D. Scholar	IIT Roorkee	2012

How to Reach:

TBA

School Short Name:

femp

Last Date Application:

Monday, August 15, 2022

School Type:

NCMW