Rectangular $C^1$-$P_k$ finite elements with $Q_k$-bubble enrichment

Paper

Abstract

We enrich the

polynomial space by

(

), or

(

), or 8 (all

)

bubble functions to obtain a family of

(

) finite elements on rectangular meshes. We show the uni-solvency, the

-continuity and the quasi-optimal convergence. Numerical tests on the new

and

, elements are performed.