Modern discretization and solution methods for time-dependent PDEs
consider the full problem in space and time simultaneously and aim to
overcome limitations of classical approaches by first discretizing in
space and then solving the resulting ODE, or first discretizing in
time and then solving the PDE in space.
The development of space-time methods for hyperbolic and parabolic
differential equation is an emerging and rapidly growing field in
numerical analysis and scientific computing. At the first Workshop on
this topic in 2017 a large variety of interesting and challenging
concepts, methods, and research directions have been presented; now we
exchange the new developments.
The focus is on the optimal convergence of
discretizations and on efficient error control for space-time methods for
hyperbolic and parabolic problems, and on solution methods with optimal
complexity. This is complemented by applications in the field of
time-dependent stochastic PDEs, non-local material laws in space and time,
optimization with time-dependent PDE
constraints, and multiscale methods for time-dependent PDEs.