1 research outputs found
Two families of -rectangle nonconforming finite elements for sixth-order elliptic equations
In this paper, we propose two families of nonconforming finite elements on
-rectangle meshes of any dimension to solve the sixth-order elliptic
equations. The unisolvent property and the approximation ability of the new
finite element spaces are established. A new mechanism, called the exchange of
sub-rectangles, for investigating the weak continuities of the proposed
elements is discovered. With the help of some conforming relatives for the
problems, we establish the quasi-optimal error estimate for the
tri-harmonic equation in the broken norm of any dimension. The
theoretical results are validated further by the numerical tests in both 2D and
3D situations