A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems.
Appeared in: IMPACT Comput. Sci. Engrg. 4, pp. 269-314 (1992)
| SC 92-05 | Jens Lang, Artur Walter
A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction-Diffusion- Systems. Appeared in: IMPACT Comput. Sci. Engrg. 4, pp. 269-314 (1992) | |
Abstract: Large scale combustion simulations show
the need for adaptive methods. First, to save computation
time and mainly to resolve local and instationary phenomena.
In contrast to the widespread method of lines, we look at
the reaction- diffusion equations as an abstract Cauchy
problem in an appropriate Hilbert space. This means, we
first discretize in time, assuming the space problems solved
up to a prescribed tolerance. So, we are able to control the
space and time error separately in an adaptive approach. The
time discretization is done by several adaptive Runge-Kutta
methods whereas for the space discretization a finite
element method is used. The different behaviour of the
proposed approaches are demonstrated on many fundamental
examples from ecology, flame propagation, electrodynamics
and combustion theory.
Keywords: initial boundary
value problem, Rothe- method, adaptive Runge-Kutta method,
finite elements, mesh refinement.
AMS
CLASSIFICATION: 65J15, 65M30, 65M50.
Keywords: initial boundary value problem,
Rothe method,
adaptive Runge-Kutta method,
finite elements,
mesh refinement
MSC: 65J15, 65M30, 65M50