Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10346030 | Computers & Mathematics with Applications | 2015 | 106 Pages |
Abstract
A unified construction of high order shape functions is given for all four classical energy spaces (H1, H(curl), H(div) and L2) and for elements of “all” shapes (segment, quadrilateral, triangle, hexahedron, tetrahedron, triangular prism and pyramid). The discrete spaces spanned by the shape functions satisfy the commuting exact sequence property for each element. The shape functions are conforming, hierarchical and compatible with other neighboring elements across shared boundaries so they may be used in hybrid meshes. Expressions for the shape functions are given in coordinate free format in terms of the relevant affine coordinates of each element shape. The polynomial order is allowed to differ for each separate topological entity (vertex, edge, face or interior) in the mesh, so the shape functions can be used to implement local p adaptive finite element methods. Each topological entity may have its own orientation, and the shape functions can have that orientation embedded by a simple permutation of arguments.
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Federico Fuentes, Brendan Keith, Leszek Demkowicz, Sriram Nagaraj,