Unformatted text preview: roduce N equally spaced elements on 0 x 1 with nodes xj = jh,
j = 0 1 : : : N (h = 1=N ). Approximate u by U having the form U (x) = N
X
j =1 ck k (x) where j (x), j = 1 2 : : : N , is the piecewise linear basis (1.3.4), and use
Galerkin's method to obtain the global sti ness and mass matrices and the
load vector for this problem. (Again, the approximation U (x) does not satisfy
the natural boundary condition u (1) = 0 nor does it have to. We will discuss
this issue in Chapter 2.)
0 22 Introduction
3.3. Write a program to solve this problem using the nite element method developed in Part 3.2b and the tridiagonal algorithm of Problem 2. Execute your
program with p = 1, q = 1, and f (x) = x and f (x) = x2 . In each case, use
N = 4, 8, 16, and 32. Let e(x) = u(x) ; U (x) and, for each value of N , compute jej , je (xN )j, and kekA according to (1.3.22) and (1.3.23a). You may
(optionally) also compute kek0 as de ned by (1.3.23c). In each case, estimate
the rate of convergence of the nite element solution...
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 Spring '14
 JosephE.Flaherty
 Numerical Analysis, Finite Element Method, Boundary value problem, Cj J, nite element

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