SC 99-20 Jens Lang: Adaptive Multilevel Solution of Nonlinear Parabolic PDE
Systems. Theory, Algorithm, and Applications
Abstract: This monograph has been written to illustrate the
interlocking
of theory, algorithm, and application in developing
solution
techniques for complex PDE systems. A deep theoretical
understanding is necessary to produce a powerful idea
leading
to a successful algorithm. Efficient and robust
implementation
is the key to make the algorithm perform satisfactorily.
The
extra insight obtained by solving real-life problems
brings out the structure of the method more
clearly and suggests often ways to improve the numerical
algorithm.
It is my intention to impart the beauty and complexity
found in both the theoretical investigation of the
adaptive
algorithm proposed here, i.e., the coupling of Rosenbrock
methods
in time and multilevel finite elements in space, and its
realization.
I hope that this method will find many more interesting
applications.
Keywords: Adaptive multilevel finite elements,
Rosenbrock methods,
a posteriori error estimates,
Rothe method
MSC: 65M60, 65C20