Unformatted text preview: 141 Infinity norm of the error at the grid points for various methods and numbers of interior grid points M M = 9 99 999 1st order finite difference 1.5702e01 1.6571e01 1.6632e01 2nd order finite difference 1.5702e01 1.6571e01 1.6632e01 Linear finite elements 1.4974e01 1.6472e01 1.6622e01 Quadratic finite elements 1.4975e01 1.6472e01 1.6622e01 Discussion: Clearly, the finite difference methods are easier to program and therefore are almost always used when x is a single variable. Finite elements become useful, though, when x has 2 or more components and the shape of the domain is nontrivial. The bulk of the work in these methods is in function evaluations. We need O ( M ) evaluations of a , c , and f in order to form each matrix. For finite differences, the constant is close to 1, but quad (the numerical integration routine) uses many function evaluations per call (on the order of 10), making formation of the finite element matrices about 10 times as expensive....
View
Full Document
 Fall '11
 Dr.Robin
 Numerical Analysis, Mathematical analysis, grid points, Linear Finite Elements, finitediff2

Click to edit the document details