Hp-finite element trace inequalities for the pyramid. (March 2015)

• Record Type: Journal Article
• Authors: Chan, Jesse; Warburton, T.
• Is Part Of: Computers & mathematics with applications. Volume 69:issue 6(2015)
• Page Start: 510
• Page End: 517
• Publication Date: 2015-03
• Subjects: Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.01.011
• Languages: English
• ISSNs: 0898-1221

Abstract

<abstract xml:lang="en" abstract-type="author" id="a000005"> <title id="st000005">Abstract</title> <sec> <p id="sp000025">Polynomial trace inequalities typically involve an unknown constant, depending on the order <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2cp1fn9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si8.gif" display="inline" overflow="scroll" id="d13e344" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math></alternatives></inline-formula> of the polynomial. The dependence of these constants on <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2cnznht" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si9.gif" display="inline" overflow="scroll" id="d13e348" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math></alternatives></inline-formula> was made more explicit in Warburton and Hesthaven (2003) for the general <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj2cp1jhp" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si10.gif" display="inline" overflow="scroll" id="d13e352" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math></alternatives></inline-formula>-simplex, and they were determined for quadrilaterals, hexes, and wedges in Hillewaert (2013). In this note, we derive explicit expressions for the constant in the trace inequality for two sets of basis functions on the pyramid.</p> </sec> </abstract>