Abstract
The convergence of a time discretisation with variable time steps is shown for a class of doubly nonlinear evolution equations of second order. This also proves existence of a weak solution. The operator acting on the zero-order term is assumed to be the sum of a linear, bounded, symmetric, strongly positive operator and a nonlinear operator that fulfils a certain growth and a Hölder-type continuity condition. The operator acting on the first-order time derivative is a nonlinear hemicontinuous operator that fulfils a certain growth condition and is (up to some shift) monotone and coercive.
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Communicated By Douglas Arnold.
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Emmrich, E., Thalhammer, M. Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order. Found Comput Math 10, 171–190 (2010). https://doi.org/10.1007/s10208-010-9061-5
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DOI: https://doi.org/10.1007/s10208-010-9061-5
Keywords
- Evolution equation of second order
- Monotone operator
- Weak solution
- Time discretisation
- Variable time grid
- Convergence