Recently, there has been a significant amount of attention given to mesh adaptation methods. Such methods adapt the mesh in response to the numerical solution of the associated partial differential equation (PDE) to efficiently capture the PDE features which typically occur at various scales.

Although there has been a strong tradition in mesh adaptation, several trends in computational physics applications represent important challenges for current mesh adaptation methods. First, sophisticated mesh adaptation methods need to be developed for use with unsteady, multiphysics flow problems. An important example of such an application is cardiac simulations involving arrhythmias. Second, local dynamic mesh refinement can be used to capture and track moving interfaces in multi-phase flows that take place in metallurgical processes. Secondly, the evolution of PDE discretization methods and algorithms requires specific mesh adaptation techniques. This is particularly true for mesh adaptation algorithms designed for massively parallel solvers, and high-order mesh adaptation methods that help exploit the full potential of recent high-order spatial discretization schemes. Finally, there is an increasing demand in the industry for simulation technologies that can be used by application engineers who possess limited numerical knowledge. In this framework, automatic mesh adaptation procedures aimed at replacing the expertise of mesh generation specialists, are seen as valuable tools. The goal of the minisymposium is to bring together researchers whose focus is on the development of advanced methods in mesh adaptation with those who apply adaptive mesh techniques to advanced applications in science and engineering. The minisymposium will feature talks by mathematicians, computer scientists, and engineers who work in the field of mesh adaptation.