A nodal type polynomial finite element exact sequence over quadrilaterals
This work provides new finite element tools for solving specific fourth-order and Brinkman problems, but the contribution is incremental as it extends existing exact sequence concepts to quadrilateral meshes.
The authors propose two nodal nonconforming finite elements over convex quadrilaterals, forming part of an exact sequence, with 12 degrees of freedom each, for solving fourth-order elliptic singular perturbation and Brinkman problems. Numerical examples demonstrate their effectiveness.
This work proposes two nodal type nonconforming finite elements over convex quadrilaterals, which are parts of a finite element exact sequence. Both elements are of 12 degrees of freedom (DoFs) with polynomial shape function spaces selected. The first one is designed for fourth order elliptic singular perturbation problems, and the other works for Brinkman problems. Numerical examples are also provided.