Finite Element Method

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The exhaustive list of topics in Finite Element Method in which we provide Help with Homework Assignment and Help with Project is as follows:

Finite Element Method. Difference between Finite Element and Finite Difference Methods.
Method of Weighted Residuals: Collocation, Method of Least squares, Galerkin’s method, Element of Calculus of Variations , Ritz Method, Equivalence of Ritz and Galerkin method for some cases.
Linear ,quadratic and higher order elements . Application to solutions of ODE. Assembly and solution of banded system.
Difference between 1D and 2D approach, types of 2D elements, Local coordinates, Global coordinates. Triangular elements: linear and quadratic elements with area coordinates Rectangular elements: General Quadrilateral elements, serendipity elements, linear and higher order shape functions.
Assembly of element equations, Solution of equations Application to flow and heat transfer problems, Discussion over higher order differential equations.
Some programming aspects: Mesh Generation, Mesh refinement, Numerical integration etc.
Meshless Galerkin methods: Difference between Meshfree and FEM methods, Choice of approach, and interpolating polynomials, variational formulation, Application to some simple problem.