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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.