Picasso, M.
An Adaptive Finite-Element Algorithm for a 2-Dimensional Stationary Stefan-Like Problem
Computer Methods in Applied Mechanics and Engineering
0045-7825
10.1016/0045-7825(95)00793-Z
124
3
213-230
An efficient adaptive algorithm is presented for a stationary regularized Stefan problem in 2D. The adaptive criteria relies upon a posteriori estimates based on the residual equation. Since the problem we are studying is a non-linear diffusion-convection problem, these error estimates are relatively crude in the sense that the constant relating the true error to the error indicator is unknown. Thus, instead of trying to build a mesh such that the true error is below a given tolerance, the local error indicator is equidistributed in a way such that the final number of triangles is close to a desired value. At each iteration of the adaptive algorithm, the new triangulation is obtained from the previous one by adding or deleting vertices according to the error indicator and a global mesh regeneration is performed using a Delaunay mesh generator. Numerical experiments for two practical situations show the efficiency and the robustness of our approach.
POSTERIORI ERROR ESTIMATORS;
PARABOLIC PROBLEMS;
LINEAR SCHEME;
SOLIDIFICATION;
IMPLEMENTATION;
TRIANGULATIONS;
SIMULATION;
EQUATIONS;
1995