caa a22 4500 606244662 CHVBK 20210128105231.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s12044-015-0232-9 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0232-9 h - p Spectral element methods for three dimensional elliptic problems on non-smooth domains, Part-I: Regularity estimates and stability theorem [Elektronische Daten] [P DUTT, AKHLAQ HUSAIN, A MURTHY, C UPADHYAY] This is the first of a series of papers devoted to the study of h-p spectral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the vertex-edge singularities. In addition, the solution is anisotropic in the neighbourhoods of the edges and vertex-edges. To overcome the singularities which arise in the neighbourhoods of vertices, vertex-edges and edges, we use local systems of coordinates. These local coordinates are modified versions of spherical and cylindrical coordinate systems in their respective neighbourhoods. Away from these neighbourhoods standard Cartesian coordinates are used. In each of these neighbourhoods we use a geometrical mesh which becomes finer near the corners and edges. The geometrical mesh becomes a quasi-uniform mesh in the new system of coordinates. We then derive differentiability estimates in these new set of variables and state our main stability estimate theorem using a non-conforming h-p spectral element method whose proof is given in a separate paper. Indian Academy of Sciences, 2015 Spectral element method nationallicence non-smooth domains nationallicence geometric mesh nationallicence vertex singularity nationallicence edge singularity nationallicence vertex-edge singularity nationallicence differentiability estimates nationallicence stability estimates nationallicence exponential accuracy nationallicence DUTT P. Department of Mathematics & Statistics, Indian Institute of Technology, 208 016, Kanpur, India aut HUSAIN AKHLAQ Department of Mathematics, The LNM Institute of Information Technology, 302 031, Jaipur, India aut MURTHY A. TIFR Centre For Applicable Mathematics, Tata Institute of Fundamental Research, 560 065, Bangalore, India aut UPADHYAY C. Department of Aerospace Engineering, Indian Institute of Technology, 208 016, Kanpur, India aut Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 239-270 0253-4142 125:2<239 2015 125 12044 https://doi.org/10.1007/s12044-015-0232-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0232-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- DUTT P. Department of Mathematics & Statistics, Indian Institute of Technology, 208 016, Kanpur, India aut NATIONALLICENCE 700 1- HUSAIN AKHLAQ Department of Mathematics, The LNM Institute of Information Technology, 302 031, Jaipur, India aut NATIONALLICENCE 700 1- MURTHY A. TIFR Centre For Applicable Mathematics, Tata Institute of Fundamental Research, 560 065, Bangalore, India aut NATIONALLICENCE 700 1- UPADHYAY C. Department of Aerospace Engineering, Indian Institute of Technology, 208 016, Kanpur, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 239-270 0253-4142 125:2<239 2015 125 12044 SWISSBIB 606244441