P. Houston, R. Hartmann

Self-adaptive Methods for PDEs

Many processes in science and engineering are formulated in terms of partial differential equations. Typically, for problems of practical interest, the underlying analytical solution exhibits localised phenomena such as boundary and interior layers and corner and edge singularities, for example, and their numerical approximation presents a challenging computational task. Indeed, in order to resolve such localised features, in an accurate and efficient manner, it is essential to exploit so-called self-adaptive methods.

Such approaches are typically based on a posteriori error estimates for the underlying discretization method in terms of local quantities, such as local residuals, computed from the discrete solution. Over the last few years, there have been significant developments within this field in terms of both rigorous a posteriori error analysis, as well as the subsequent design of optimal meshes. In this minisymposium, a number of recent developments, such as the design of high-order and hp-adaptive finite element methods will be considered, as well as anisotropic mesh adaptation and mesh movement.