Computational experiments using nonconforming finite elements



Journal Title

Journal ISSN

Volume Title


Texas Tech University


Initially, the conforming finite element method is explained. The steps of the finite element method (begin with a second-order differential equation, multiply by a test function, put in integral form, produce a weak formulation by integrating by parts, reach a system of equations, and solve for unknowns) are discussed for a simple univariate case, general univariate case, and Poisson’s equation^1.

A nonconforming finite element method is then used to solve the two-dimensional Poisson's equation. A matlab code, which may be found in the Appendix section A3 , solves the problem on Ù = [—1,1] x [0,1], where Ù1 = [—1.0] x [0,1] and Ù2 = [0,1] X [0,1]. The approximation on the boundary Ã12 =Ù1Ù2 is not truly continuous, but is “weakly" continuous. The result is a discontinuous approximation to a smooth function that demonstrates the feasibility of solving Poisson's equation by combining two separately meshed regions and enforcing "weak" continuity across the boundary.