Isogeometric discrete differential forms: Non-uniform degrees, Bézier extraction, polar splines and flows on surfaces

• Published in: Computer methods in applied mechanics and engineering Vol. 376; p. 113576
• Main Authors: Toshniwal, Deepesh, Hughes, Thomas J.R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2021; Elsevier BV
• Subjects: Algorithms; Bezier patches; Computational fluid dynamics; Conservation laws; Degree elevation; Fluid flow; Fluid mechanics; Incompressible flow; Mathematical analysis; Numerical methods; Optimal approximation; Partial differential equations; Pointwise incompressibility; Robustness (mathematics); Singularly parametrized surfaces; Smooth splines; Stokes flow; Surface flows; Tensors; The de Rham complex; Pointwise incompressibility; Optimal approximation; Smooth splines; Surface flows; The de Rham complex; Singularly parametrized surfaces

Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass co...