The finite-difference approach with equidistant grids is easy to understand and straightforward to implement. The resulting uniform rectangular grids are comfortable, but in many applications not flexible enough. Steep gradients of the solution require a finer grid such that the difference quotients provide good approximations of the differentials. On the other hand, a flat gradient may be well modeled on a coarse grid. Such a flexibility of the grid is hard to obtain with finite-difference methods.
KeywordsWeak Solution Bilinear Form Weighted Residual Homogeneous Boundary Condition Element Matrice
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- 1.In this subsection the meaning of the index 0 is twofold: It is the index of the “first” hat function, and serves as symbol of the homogeneous boundary conditions (5.21b).Google Scholar