Analysis of a combined NC1-C2 method for elliptic problem
This is an incremental improvement for numerical analysts working on finite element methods for elliptic PDEs.
The paper presents a combined NC1-C2 finite element method for elliptic problems, showing that the new element behaves like a P1 non-conforming element and achieves theoretical error estimates confirmed by numerical results.
It is shown in this paper that non-conforming finite elements on the triangle using $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials can be easily built and used.They appear as an 'enriched' version of the standard piecewise quadratic six-node element.This work is divided into two parts.In the first we present the basic- property of the element,namely how it can be built and basic error estimates.We have observed that this new element behaves like $P^{1}$ non-conforming element.In the second part we have applied our element to the elliptic problem and the theoretical estimate has been guaranteed by numerical result.