Читать книгу Finite Element Analysis - Barna Szabó - Страница 17

1 The definition of the integral by eq. (1.8) made it possible to find an approximation to the exact solution u of eq. (1.5) without knowing u.

2 A formulation cannot be meaningful unless all indicated operations are defined. In the case of eq. (1.5) this means that and are finite on the interval . In the case of eq. (1.11) the integralmust be finite which is a much less stringent condition. In other words, eq. (1.8) is meaningful for a larger set of functions u than eq. (1.5) is. Equation (1.5) is the strong form, whereas eq. (1.11) is the generalized or weak form of the same differential equation. When the solution of eq. (1.5) exists then un converges to that solution in the sense that the limit of the integral is zero.

3 The error depends on the span and not on the choice of basis functions.