Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
Repin, S. (2019). Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods. In B. N. Chetverushkin, W. Fitzgibbon, Y. Kuznetsov, P. Neittaanmäki, J. Periaux, & O. Pironneau (Eds.), Contributions to Partial Differential Equations and Applications (pp. 411-432). Springer. Computational Methods in Applied Sciences, 47. https://doi.org/10.1007/978-3-319-78325-3_22
Julkaistu sarjassa
Computational Methods in Applied SciencesTekijät
Toimittajat
Päivämäärä
2019Tekijänoikeudet
© Springer International Publishing AG, part of Springer Nature 2019
We consider inequalities of the Poincaré–Steklov type for subspaces of H1 -functions defined in a bounded domain Ω∈Rd with Lipschitz boundary ∂Ω . For scalar valued functions, the subspaces are defined by zero mean condition on ∂Ω or on a part of ∂Ω having positive d−1 measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of ∂Ω (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincaré type inequalities for domains typically used in finite element methods (triangles, quadrilaterals, tetrahedrons, prisms, pyramids, and domains composed of them). The second part of the paper discusses applications of the estimates to interpolation of scalar and vector valued functions on macrocells and on meshes with non-overlapping and overlapping cells.
Julkaisija
SpringerEmojulkaisun ISBN
978-3-319-78324-6Kuuluu julkaisuun
Contributions to Partial Differential Equations and ApplicationsISSN Hae Julkaisufoorumista
1871-3033Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/28186004
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
Lohi, Jonni (Springer, 2022)We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to ... -
Malliavin smoothness on the Lévy space with Hölder continuous or BV functionals
Laukkarinen, Eija (2020)We consider Malliavin smoothness of random variables f(X1), where X is a purejump Lévy process and the functionfis either bounded and Hölder continuousor of bounded variation. We show that Malliavin differentiability and ... -
Vector database management systems : Fundamental concepts, use-cases, and current challenges
Taipalus, Toni (Elsevier, 2024)Vector database management systems have emerged as an important component in modern data management, driven by the growing importance for the need to computationally describe rich data such as texts, images and video in ... -
A Surrogate-assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-objective Optimization
Chugh, Tinkle; Jin, Yaochu; Miettinen, Kaisa; Hakanen, Jussi; Sindhya, Karthik (Institute of Electrical and Electronics Engineers, 2018)We propose a surrogate-assisted reference vector guided evolutionary algorithm (EA) for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed ... -
Instruction-based clinical eye-tracking study on the visual interpretation of divergence : how do students look at vector field plots?
Klein, P.; Viiri, Jouni; Mozaffari, S.; Dengel, A.; Kuhn, J. (American Physical Society, 2018)Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.