Abstract
Adaptive mesh refinement techniques are well established and widely used for space discretizations. In contrast, local time stepping is much less used, and the corresponding techniques are less mature, needing delicate synchronization steps, which involve interpolation, extrapolation or projection. These operations can have adverse effects on the stability, and can also destroy important geometric properties of the scheme, like for example the conservation of invariants. We give here a survey on the intensive research performed in this direction over the last two decades.
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Keywords
- Discontinuous Galerkin Method
- Domain Decomposition Method
- Adaptive Time
- Richardson Extrapolation
- Linear Multistep Method
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Gander, M.J., Halpern, L. (2013). Techniques for Locally Adaptive Time Stepping Developed over the Last Two Decades. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_44
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