We know that there is a finite element solver process routine
1. Galerkin Solution + Green-Guass formula. Neumann boundary conditions will naturally meet, no subsequent correction boundary conditions
2. For a triangular cell, we generally use the area map coordinates solved. Is used for two-dimensional rectangular unit associated with the center point of the rectangular coordinate mapping, the mapping results of an integration interval [1,1], [- 1,1] is a square of 2.
3. Select the interpolation function: a first order interpolation formula
4. The interpolation function can be substituted into the calculation.
The second-order interpolation function is calculated for the rectangular unit
6. Here add correction boundary conditions, a natural Neumann boundary conditions satisfied, the first boundary condition necessary stiffness matrix boundary point numbers where the row and column to 0, set to 1 the diagonal, while the load matrix be amended accordingly. Both are relatively simple boundary conditions. For the third boundary condition, which method is applied:
Following the last integral equation is calculated, and wherein Hi Bij function on the boundary of the integral to be calculated. We know that, even at the border, the border is by a small number of units enclosed. Therefore, like the third boundary condition than the first boundary condition that the value of a single node to operate, but with the side units, a calculation of an edge of a cell by integrating two consecutive nodes. Line and also used when calculating map coordinates thus calculated more convenient. Note that different positions in the cell boundary, the results are different, as in each cell, the cell number of the node points 1,2,3, if the boundary side edge node unit 12, the calculation result to the node 23 side, edge 13 are different. For edge 12, phi1 = 1-epsilon; phi2 = epsilon; phi3 = 0. See below can be further appreciated that in FIG.
