Picasso, M.
An Adaptive Finite-Element Algorithm for a 2-Dimensional Stationary Stefan-Like Problem
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
124
3
POSTERIORI ERROR ESTIMATORS
PARABOLIC PROBLEMS
LINEAR SCHEME
SOLIDIFICATION
IMPLEMENTATION
TRIANGULATIONS
SIMULATION
EQUATIONS
1995
1995
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.
0045-7825
Computer Methods in Applied Mechanics and Engineering
Picasso, m, ecole polytech fed lausanne,dept math,ch-1015 lausanne,switzerland.
Journal Articles
10.1016/0045-7825(95)00793-Z