Adaptive Finite Elements. Performance, convergence and optimality

PEDRO MORIN

Rio de Janeiro

Encuentro; Seminário Científico MathAmSud; 2009

Finite elements are a well-established tool for the numerical solution of boundary value problems. Adaptivity started in the late 1970's, and often allows for a much more efficient use of the computational resources; for certain problems, it is even indispensable to their numerical solvability. In this talk I will present the basic ideas underlying adaptivity, and will show its potential through some illustrating simulations. Finally I will mention convergence and optimaliry results that have been obtained in the last few years.