4.2.1.2 A Posteriori Mesh Refinement

Since an edge refinement algorithm can not be used to enforce the angle criterion (4.1) we use a different approach to enforce the Minimax principle. Starting at time step $t_0$ the simulation is performed as follows.

(1)

Compute the actual time step. Keep values of previous time step.

(2)

The concentration of all dopant species is investigated. If no negative concentrations are found save the computed concentrations for later reference, increase the time step, and continue at ($1$).

(3)

Recursively refine $10\%$ of the edges with the biggest gradient of the concentration.

(4)

Take over values of previous time step and go to ($1$).

Although the algorithm is not (theoretically) guaranteed to terminate since it can not repair a violated angle criterion, the practical application shows that it effectively avoids negative concentrations.

2003-03-27