An Adaptive Finite-Element Algorithm for a 2-Dimensional Stationary Stefan-Like Problem
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.
Picasso, m, ecole polytech fed lausanne,dept math,ch-1015 lausanne,switzerland.
ISI Document Delivery No.: RM289
Times Cited: 5
Cited Reference Count: 48
Record created on 2006-08-24, modified on 2016-08-08