Shangyou Zhang

collaborators

6 papers

math.NA2025

Rectangular $C^{1}$ - $P_{k}$ finite elements with $Q_{k}$ -bubble enrichment

Shangyou Zhang

We enrich the $P_{k}$ polynomial space by $5$ ( $k = 4$ ), or $7$ ( $k = 5$ ), or 8 (all $k \geq 6$ ) $Q_{k}$ bubble functions to obtain a family of $C^{1}$ - $P_{k}$ ( $k \geq 4$ ) finite elements on rect…

math.NA2025

$C^{1}$ - $Q_{k}$ serendipity finite elements on rectangular meshes

Shangyou Zhang

A $C^{1}$ - $Q_{k}$ serendipity finite element is a sub-element of $C^{1}$ - $Q_{k}$ BFS finite element such that the element remains $C^{1}$ -continuous and includes all $P_{k}$ polynomials. In ot…

math.NA2025

Rectangular $C^{1}$ - $Q_{k}$ Bell finite elements in two and three dimensions

Hongling Hu, Shangyou Zhang

Both the function and its normal derivative on the element boundary are $Q_{k}$ polynomials for the Bogner-Fox-Schmit $C^{1}$ - $Q_{k}$ finite element functions. Mathematically, to keep th…

math.NA2025

A nodal basis for the $C^{1}$ - $P_{33}$ finite elements on 5D simplex grids

Jun Hu, Shangyou Zhang

We construct a nodal basis for the 5-dimensional $C^{1}$ finite element space of polynomial degree $33$ on simplex grids, where the finite element functions are $C^{1}$ on the 6 4D-sim…

math.NA2025

Superconvergent quadriatic finite element on uniform tetrahedral meshes

Yunqing Huang, Shangyou Zhang

By a direct computation, we show that the $P_{2}$ interpolation of a $P_{3}$ function is also a local $H^{1}$ -projection on uniform tetrahedral meshes, i.e., the difference is $H^{1}$ -orth…

math.NA2025

Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes

Shangyou Zhang

We extend the $C^{1}$ - $P_{3}$ Fraeijs de Veubeke-Sander finite element to two families of $C^{1}$ - $P_{k}$ ( $k > 3$ ) macro finite elements on general quadrilateral meshes. On each quadrilater…

Rectangular C1-Pk​ finite elements with Qk​-bubble enrichment

C1-Qk​ serendipity finite elements on rectangular meshes

Rectangular C1-Qk​ Bell finite elements in two and three dimensions

A nodal basis for the C1-P33​ finite elements on 5D simplex grids

Superconvergent quadriatic finite element on uniform tetrahedral meshes

Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes

Rectangular $C^{1}$ - $P_{k}$ finite elements with $Q_{k}$ -bubble enrichment

$C^{1}$ - $Q_{k}$ serendipity finite elements on rectangular meshes

Rectangular $C^{1}$ - $Q_{k}$ Bell finite elements in two and three dimensions

A nodal basis for the $C^{1}$ - $P_{33}$ finite elements on 5D simplex grids