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Advanced Finite Element Analysis: Course Outline (642)

Course Contents

Introduction to Sobolev spaces, Ritz-Galerkin approximation of Poisson’s equation, weak form of Poisson’s equation, variational form of Poisson’s equation, Ritz-Galerkin approximation of Poisson’s equation with hat functions, elliptic bilinear form, elliptic variational form, Ritz-Galerkin approximation of an elliptic variational problem, construction of FE basis, properties of basis function, basis function of multidimensional space, linear independence of basis function, basis function on uniform grid, condition number of Galerkin matrix, uniform Lagrange polynomial, extension of basis function, coefficients of extended basis, weight functions, R-functions, partial weight function, WEB-splines, stability and approximation with WEB-spline, Ritz-Galerkin system, applications of WEB-approximation.

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