In the following two examples are presented. In the first the well-known model equation for diffusion
The first example (Fig. 4.10 and Fig. 4.11) depicts a cube with elements which was refined to elements during the simulation. Both figures depict the result after the same time. Fig. 4.10 illustrates the unrefined case. Negative concentrations emerged and the symmetry of the Gaussian profile is violated. Fig. 4.11 shows the result of the simulation with the refinement algorithm turned on. Negative concentrations are not visible.
The second example demonstrates the locality of the implemented refinement algorithm. Fig. 4.12 displays a part of the schematic transistor cell of Fig. 4.4. The aim of this example was to locally refine the gate region. To achieve this local refinement all edges within a rectangular region around the gate were marked for refinement. Fig. 4.13 depicts the final mesh after the refinement was performed. The locality of the refinement algorithm is clearly visible.