Numerical Modeling has reached an amazing level of maturity: scientists and engineers use it as complement to Experimental Modeling and analysis and as a design tool in an extremely wide variety of problems. However, the user often forgets that answers provided by Numerical Models are affected by errors. The problem of assessing and controlling the quality of the numerical solutions is far of being solved for arbitrary models and it is in fact one of the challenges in computational mechanics for the next future. The adaptive strategies pertain to the techniques providing quality control with a minimum computational effort
SIAM comment on the Simulation-Based Engineering Science Report by a blue-ribbon panel of experts commisioned by theNational ScienceFoundation, see http://www.siam.org/about/news-siam.php?id=792 , highlights the fact that in this area, "Research opportunities are described in areas like multiscale modeling and simulation, verification and validation, uncertainty quantification, and data-driven simulations".
The line of research in adaptivity and error estimation is one of the assets of LaCàN.