Weblowest-order case k “ 1 is studied. Therein a novel scheme was suggested which preserves the features of the H1-conforming formulation while using a simple lowest-order Raviart– Thomas enrichment. It turns out that there are for k ě 2 new aspects in the construction of the method and additional difficulties in their numerical analysis. WebApr 10, 2014 · It is shown that the optimal order of convergence is retained from the lowest-order case if a parametric version of Raviart--Thomas elements is used, and this is illustrated numerically for an elliptic boundary value problem involving a circular boundary curve. With this paper, our investigation of the finite element approximation on curved …
[PDF] Numerical Analysis Approximation properties of …
Web3. A modified Raviart–Thomas (MRT) space of the lowest order Let W h be the space of functions which are piecewise constant on T h. To define V h, let V hðQ^Þ denote the local space on the reference element Q^ consisting of all functions of the form: ^v ¼ a þb^xþð dÞ b 2jQj ^xð^ 1 ;c ^y þðbþdÞ c 2jQj ^yð^y 1Þ; WebBasic interpolation results are settled for lowest-order hexahedral Raviart–Thomas finite elements. Convergence in H(div) is proved for regular families of asymptotically parallelepiped meshes. The need of the asymptotically parallelepiped assumption is demonstrated with a numerical example. To cite this article: A. Bermúdez et al., C. R. … cip ph
Approximation properties of lowest-order hexahedral Raviart-Thomas …
WebMay 1, 2005 · Basic interpolation results are settled for lowest-order hexahedral Raviart–Thomas finite elements. Convergence in H ( div) is proved for regular families of … WebBasic interpolation results are settled for lowest-order hexahedral Raviart-Thomas finite elements. Convergence in H(div) is proved for regular families of asymptotically … WebRaviart) as well as vector-valued (e.g., Raviart-Thomas) elements. The interpo lation properties are given for both smooth and nonsmooth functions (Clement inter polation, Scott-Zhang interpolation) and also for domains with curved boundaries. Galerkin approximation and related topics (Lax-Milgram, Aubin-Nitsche, and Strang dialysis infection rates