caa a22 4500 378847813 CHVBK 20180305123315.0 cr unu---uuuuu 161128e20030601xx s 000 0 eng 10.1515/156939803322380846 doi (NATIONALLICENCE)gruyter-10.1515/156939803322380846 New mixed finite element method on polygonal and polyhedral meshes [Elektronische Daten] [Yu. Kuznetsov, S. Repin] In the framework of mixed and hybrid finite element methods for diffusion-type and other elliptic differential equations, it is necessary to apply numerical schemes with variables given as values of normal fluxes on the edges (faces) of the elementary cells and values of the scalar-valued function in each cell. In this paper, we propose a general method of constructing finite element approximations on polygonal and polyhedral meshes, whose cells are convex and nonconvex polygonal domains in and polyhedrons in . We present a natural way of constructing cell prolongation operators, which makes it possible to easily compute the coefficients of the respective mass matrices. Also, the proposed prolongations satisfy the important requirement that the image of the divergence operator on the extended fields belongs to the set of piecewise constant functions. The latter fact provides direct justification of the well-posedness of the arising discrete problems. Copyright 2003, Walter de Gruyter Kuznetsov Yu University of Houston, Mathematical Department, 4800 Culhoun Road, Houston, Texas 77204, USA aut Repin S. St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg 191011, Russia aut Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 261-278 0927-6467 18:3<261 2003 18 rnam https://doi.org/10.1515/156939803322380846 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939803322380846 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kuznetsov Yu University of Houston, Mathematical Department, 4800 Culhoun Road, Houston, Texas 77204, USA aut NATIONALLICENCE 700 1- Repin S. St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg 191011, Russia aut NATIONALLICENCE 773 0- Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 261-278 0927-6467 18:3<261 2003 18 rnam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter