Adaptive computation with splines on triangulations with hanging vertices. (English) Zbl 1385.65019
Fasshauer, Gregory E. (ed.) et al., Approximation theory XV: San Antonio 2016. Selected papers based on the presentations at the international conference, San Antonio, TX, USA, May 22–25, 2016. Cham: Springer (ISBN 978-3-319-59911-3/hbk; 978-3-319-59912-0/ebook). Springer Proceedings in Mathematics & Statistics 201, 197-218 (2017).
Summary: It is shown how computational methods based on Bernstein-Bézier methods for polynomial splines on triangulations can be carried over to compute with splines on triangulations with hanging vertices. Allowing triangulations with hanging vertices provides much more flexibility than using ordinary triangulations and allows for simple adaptive algorithms based on local refinements. The use of these techniques is illustrated for two application areas of splines – namely, function fitting and the solution of boundary value problems.
For the entire collection see [Zbl 1378.65012].
For the entire collection see [Zbl 1378.65012].
MSC:
| 65D07 | Numerical computation using splines |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
Keywords:
spline functions; hanging vertices; adaptive methods for fitting; adaptive finite elements; Ritz-Galerkin method; error estimates; numerical experiment; Bernstein-Bézier methods; algorithm; boundary value problemsSoftware:
SplinePakReferences:
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