# hw4_98W - HW#2 1 Homework#4 AM 502 Differential Equation...

This preview shows pages 1–2. Sign up to view the full content.

Homework #4 AM 502 Differential Equation Methods in Mechanics 1998 Winter, Kikuchi 1. Consider an oscillatory coefficient shown in below 0.1 0.2 0.3 0.4 x a(x) 0.5 1.0 1.5 and the functional F u ( 29 = 1 2 a x ( 29 du dx 2 + sin 2 π x ( 29 u 2 dx 0 1 - 1 + x 2 ( 29 udx 0 1 for the minimization problem min u F u ( 29 among the admissible functions such that u 0 ( 29 = u 1 ( 29 = 0 . (1) Find the first variation δ F of the functional F and its Euler’s equation by setting δ F = 0 for every δ u = 0. (2) Find the homogenized coefficient a H and homogenized functional F H u H ( 29 , and then solve the homogenized problem to find u H that minimizes the homogenized functional F H u H ( 29 . Furthermore, estimate the maximum difference of u H - u and d dx u - u H ( 29 based on the homogenization asymptotic expansion. (3) Solve the original problem by FEM or FDM, and compare these results with the one obtained by the homogenization method. 2.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 12/08/2011.

### Page1 / 2

hw4_98W - HW#2 1 Homework#4 AM 502 Differential Equation...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online