ABSTRACT
One of the important requirements that modern software must meet today is to judge the quality of its numerical approximations in order to assess safely the modeling process. Adaptive methods have proven to work efficiently providing a posteriori error estimates and appropriate strategies to improve the accuracy where needed. They are now entering into real-life applications and starting to become a standard feature in simulation programs. This chapter reports on one successful way to construct discretization methods adaptive in space and time, which are applicable to a wide range of practically relevant problems.
