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Delft, Netherlands

Hiemstra R.,Kluyverweg | Huijsmans R.,Mekelweg | Gerritsma M.,Kluyverweg
ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers | Year: 2012

Conservation laws in for example electromagnetism, solid and fluid mechanics, allow an exact discrete representation in terms of line, surface and volume integrals. We develop high order interpolants, from any basis that is a partition of unity, that satisfy these integral relations exactly, at cell level. The resulting gradient, curl and divergence conforming spaces have the property that the conservation laws become completely independent of the basis functions. This means that the conservation laws are exactly satisfied even on curved meshes. As an example, we develop high order gradient, curl and divergence conforming spaces from NURBS-non uniform rational B-splines - and thereby generalize the compatible spaces of B-splines developed by Buffa et al. [16]. We give several examples of 2D Stokes flow calculations which result, amongst others, in a point wise divergence free velocity field.

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