3687502168 - Chapter 6 Finite-Element Method Finite element...

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1 Chapter 6 Finite-Element Method Finite element method (FEM) provides an alternative to finite-difference (FD) methods, especially for systems with irregular geometry, unusual boundary conditions, or heterogeneous composition. • This method divides the solution domain into simply shaped regions or elements. An approximate solution for the PDE can be developed for each element. • The total solution is generated by linking together, or “assembling,” the individual solutions taking care to ensure continuity at the interelement boundaries. 2 Model FD FEM
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3 Introduction Finite difference : governing eq. approximately satisfied at each grid point, e.g. 22 0 TT V xy ∂∂ = += but V = 0 between the grid points? Not in high order polynomial fit! (Most finite difference schemes are based on Taylor expansion) Finite element : seeks to satisfy V =0 indirectly in integrated sense. But is V =0 satisfied at any point? 0 R Vd x d y φ = ∫∫ 4 If there is a set of functions which can approximate any continuous
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This note was uploaded on 08/27/2010 for the course ME ME4906 taught by Professor Dr.g.p.zheng during the Spring '10 term at NYU Poly.

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3687502168 - Chapter 6 Finite-Element Method Finite element...

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