Optimal Constrained Interpolation in Mesh-Adaptive Finite Element Modeling
| Autor: | Hannah R Hiester, James R. Maddison |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010504 meteorology & atmospheric sciences
Applied Mathematics Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Trilinear interpolation 010502 geochemistry & geophysics 01 natural sciences Finite element method Mathematics::Numerical Analysis REF-ready metadata Computational Mathematics Nearest-neighbor interpolation Incompressible flow Norm (mathematics) Piecewise Galerkin method ComputingMethodologies_COMPUTERGRAPHICS 0105 earth and related environmental sciences Mathematics Interpolation |
| Zdroj: | Maddison, J R & Hiester, H R 2017, ' Optimal constrained interpolation in mesh-adaptive finite element modelling ', SIAM Journal on Scientific Computing, vol. 39, no. 5, pp. A2257-A2286 . https://doi.org/10.1137/15M102054X |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/15m102054x |
| Popis: | Mesh-to-mesh Galerkin $L^2$ projection allows piecewise polynomial unstructured finite element data to be interpolated between two nonmatching unstructured meshes of the same domain. The interpolation is by definition optimal in an $L^2$ sense, and subject to fairly weak assumptions conserves the integral of an interpolated function. However other properties, such as the $L^2$ norm, or the weak divergence of a vector-valued function, can still be adversely affected by the interpolation. This is an important issue for calculations in which numerical dissipation should be minimized, or for simulations of incompressible flow. This paper considers extensions to mesh-to-mesh Galerkin $L^2$ projection which are $L^2$ optimal and ensure exact conservation of key discrete properties, including preservation of both the $L^2$ norm and the integral, and preservation of both the $L^2$ norm and weak incompressibility. The accuracy of the interpolants is studied. The utility of the interpolants is studied via adaptive mesh simulations of the two-dimensional lock-exchange problem, which are simulated using a combination of Fluidity and the FEniCS system. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|