HOMEWORK 6_W13(1) - DREXEL UNIVERSITY Department of...

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Unformatted text preview: DREXEL UNIVERSITY Department of Mechanical Engineering & Mechanics Applied Engineering Analytical & Numerical Methods II MEM 592 - Winter 2013 HOMEWORK #6: Due Thursday, February 28 @ 630pm 1. [20 points] Given is the BVP: 0, 0 0, 0 (1) 0 , i) Derive the weak formulation. ii)Write its variational form. 2. [40 points] Given is the BVP: , i) 0 0, 1 0 0, 0 1 (2) Provide its exact solution. ii) Implement the variational formulation using the approximation , where is a globally defined piecewise trial function defined below , 1 1 0 h 0 2 x, 2 2h Present all analytical computations, compute the solution at 0.5 and compare it with the exact value. iii) Use the weak formulation for the BVP in (2) with Galerkin's method and the approximation 1 1 , 1 and ∑ where . Present all analytical computations, form a linear system of 0.5 and compare it with the exact value. Which of the methods defined in equations, compute the solution at questions ii) and iii) approximates the exact solution better? Explain. 3. [40 points] Given is the BVP: , 0 0, 1 0 0, 0 1 (3) Provide a solution using a finite element scheme based on the weak formulation and Galerkin's method using a total of 2 elements (i.e. 3 nodes) and piecewise continuous shape functions in each element of the form 1 where solution , 0 is defined as a local distance in each finite element and h is their size. Compare your results with the exact . ...
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  • Spring '14
  • Numerical Analysis, Continuous function, Applied Engineering Analytical & Numerical Methods II, weak formulation

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