Abstract
Compatible or mimetic numerical methods typically use vector components as the primary unknowns in the discretization. It is frequently necessary or useful to be able to recover vectors from these spatially dispersed vector components. In this paper we discuss the relationship between a number of low order vector reconstruction methods and some preliminary results on higher order vector reconstruction. We then proceed to demonstrate how explicit reconstruction can be used to define discrete Hodge star interpolation operators, and how some reconstruction approaches can lead to local conservation statements for vector derived quantities such as momentum and kinetic energy.
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Perot, J.B., Vidovic, D., Wesseling, P. (2006). Mimetic Reconstruction of Vectors. In: Arnold, D.N., Bochev, P.B., Lehoucq, R.B., Nicolaides, R.A., Shashkov, M. (eds) Compatible Spatial Discretizations. The IMA Volumes in Mathematics and its Applications, vol 142. Springer, New York, NY. https://doi.org/10.1007/0-387-38034-5_9
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DOI: https://doi.org/10.1007/0-387-38034-5_9
Publisher Name: Springer, New York, NY
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