BAIL 2006 Book of Abstracts - Institut für Numerische und ...

Speaker:
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.
• Ralf Hartmann: Discontinuous Galerkin methods for compressible flows: higher
order accuracy, error estimation and adaptivity
• Vincent Heuveline: On a new refinement strategy for adaptive hp finite element
method
• John Mackenzie: A Discontinuous Galerkin Moving Mesh Method for Hamilton-
Jacobi Equations
• Simona Perotto: Layer Capturing via Anisotropic Mesh Adaption
• Rene Schneider: Anisotropic mesh adaption based on a posteriori estimates and
optimisation of node positions