Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IIT ISM Dhanbad

Introduction to tensors, linear dependence and independence of vectors, strong form of a differential equation, primary and secondary variables in a continuum problem, concept of variational methods, illustration of Rayleigh-Ritz, least squares, collocation, Galerkin and Petrov-Galerkin methods, limitations of variational methods, development of finite element method from the basic variational method

The Green-Gauss theorem, weak form of a differential equation, the functional, weight and shape functions, displacements or degrees-of-freedom, types of boundary conditions, domain discretization and generation of nodes, elements, structured and unstructured meshes, bar element, triangular and quadrilateral elements, Pascal’s triangle, element connectivity and assembly using IEN (Identification of Element Nodes), ID (Identification) and LM (Location Matrix) arrays

The concepts of local and global coordinates, Galerkin finite-element method, comparison of finite element solutions of one-dimensional elliptic partial differential equations of heat conduction with solutions using alternate methods, such as, finite difference and finite volume

Isoparametric elements, natural coordinates, coordinate transformation, numerical integration, computation of element level matrices and vectors through local coordinates and by Gauss quadrature for one and two-dimensional elliptic partial differential equations of heat conduction

Implementation of essential, natural and convective boundary conditions for elliptic partial equations of heat conduction in one- and two-dimensions, assembly of element level matrices and vectors and generation of the global/assembled matrix equation system of linear algebraic equations, properties of the assembled matrix equation system,

Basic matrix equation solvers for symmetric and asymmetric linear matrix equation systems, solution of the matrix equation system, concepts of preconditioners and matrix-free methods

FEM discretization of parabolic partial differential equations of heat conduction corresponding to unsteady equations, the trapezoidal rule: implicit and explicit formulations

Introduction to convective transport, the linear convection-diffusion equation, Galerkin formulation of the one-dimensional convection-diffusion equation using linear and quadratic elements, asymmetry in convection-diffusion matrix versus symmetry in conduction (diffusion) matrix, difference in banded structure of the coefficient matrix of convection-diffusion and diffusion matrices, solution of the convection-diffusion matrix equation system

Limitations of Galerkin method for flow problems, illustration of odd-even decoupling of solutions in one-dimension for high Peclet number, the need for stabilization of the weak form of flow equations, the streamline-upwind Petrov Galerkin (SUPG) stabilization, Petrov-Galerkin formulation for one-dimensional convection-diffusion equation using linear bar elements

Introduction of multiple degrees-of-freedom problems, i.e. the Navier-Stokes (N-S) equations of motion, surface traction vector, stress-divergence form of N-S equations, coupled versus segregated formulation of NavierStokes equations, Q1Q0 and Q1Q1 bilinear quadrilateral elements or staggered and collocated arrangements of primitive variables, connectivity and assembly of element level equations for multiple degrees-of-freedom problems