IST - Theory and Numerics of PDE (2025)

Speakers and Syllabus

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Satyanarayana Engu
Dept. of Mathematics,
NIT Warangal Telangana

6

Classical PDE:

  1. Laplace equation: Harmonic functions, maximum principle, fundamental solution, Green’s function and the solvability of Dirichlet problem.

  2. Heat equation: Weak and strong maximum principles for the heat equation, fundamental solution, existence and uniqueness for the initial value problem.

Manas R Sahoo
School of Mathematical sciences,
NISER, Bhubaneswar, Odisha

6

Sobolev spaces, definitions, examples, approximation and extension, basic properties, Traces, Sobolev inequalities and compact embedding’s, Poincares inequlities.

Veerappa Gowda G. D.,
TIFR Centre for Applicable Mathematics, Bengaluru

6

Non-linear hyperbolic conservation laws: Concept of weak solutions, entropy condition and uniqueness of the solution. Construction of Godunov, Lax- Friedrichs, Engquist-Osher and Lax-Wendroff schemes. Lax-Wendroff theorem for convergence of the numerical solution. Finite volume schemes. Monotone schemes: L1 stability, total variation diminishing property and their convergence to the entropy solution. Higher order schemes.
Finite volume schemes in higher dimensions.

Thirupathi Gudi Department of Mathematics, Indian Institute of Science, Bengaluru

6

Finite Element Methods: Construction of finite ele- ment spaces, Polynomial approximation/interpolation theory, FEM for elliptic problems. Finite difference in time and finite elements in space for heat and wave equations. Error analysis.FEM implementation in MATLAB.

 

 References:

  1.  L. C. Evans. Partial Differential Equations, AMS.
  2.  S. Kesavan. Topics in Functional Analysis and Applications, New Age Int. Publ.
  3.  S.    Larsson    and V. Thomee. Partial differential equations with numerical methods. Springer.
  4.  1. R.L. Burden and J.D. Faires, Numerical Analysis, Brooks/Cole, Cengage Learning, 2011
  5.  J. W. Thomas, Numerical Partial Differential Equations, Springer Science 1995.
  6.  R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhauser, Verlag, 1992
  7.  Godlewski E. and P.A. Raviart, Hyperbolic systems of conservation laws, Mathematiques et Applications, ellipses, Paris, 1991.

Time Table

 

Day

Date

Lecture 1

(9.30–11.00)

Tea
(11.00–11.30)

Lecturer 2

(11.30–1.00)

Lunch

(1.00–

2.30)

Tutorial 1

(2.30–3.30)

Tea

(3.30-

4.00)

Tutorial 2

(4.00-5.00)

Snacks 5.00-5.30

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker/ tutor)

 

(name of the speaker/ tutor)

 

Mon

01/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

Tues

02/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

Wed

03/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

Thu

04/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

Fri

05/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

Sat

06/09/ 2025

SN

Tea

MS

Lunch

MS+KD+AG

Tea

SN+AG+KD

Snacks

 SUNDAY

Mon

08/09/ 2025

VG

Tea

TG

Lunch

VG+AK+SJ

Tea

TG+ SJ +AK

Snacks

Tues

09/09/ 2025

VG

Tea

TG

Lunch

VG+AK+ SJ

Tea

TG+ SJ +AK

Snacks

Wed

10/09/ 2025

VG

Tea

TG

Lunch

VG+AK+ SJ

Tea

TG+ SJ +AK

Snacks

Thu

11/09/ 2025

VG

Tea

TG

Lunch

VG+AK+ SJ

Tea

TG+ SJ +AK

Snacks

Fri

12/09/ 2025

VG

Tea

TG

Lunch

VG+AK+ SJ

Tea

TG+ SJ +AK

Snacks

Sat

13/09/ 2025

VG

Tea

TG

Lunch

VG+AK+ SJ

Tea

TG+ SJ +AK

Snacks

 

 

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