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Line 153: If one chooses a finite element basis (using, for instance, the triangular elements discussed above) so that each test function is supported on a small number of elements then one can see that the matrices P and Q will be ''sparse'' -- that is, most of the entries are zero. Then the calculation Qb can be done in O(n) time, and solving for a can be done efficiently using an iterative algorithm (such as the [[Conjugate gradient iteration]]). We note that the choice of piecewise linear elements is not even once differentiable, however it is [[piecewise differentiable]]. It is interesting to study how such solutions converge to the real solution of the Laplace problem as the number of elements tends to infinity. [[ja:有限要素法]]

Finite element method: Difference between revisions