A nonconforming covolume method for elliptic problems

We consider a control volume(covolume) method for second order elliptic PDEs with the rotated-Q1 nonconforming finite element on rectangular grids. The coefficient may a variable, diagonal tensor, or discontinuous. We prove first order convergence in H1 norm and second order convergence in L2 norm when the partition is square. Our numerical experiments show that our covolume scheme has about 30% less error than FEM even when is discontinuous tensor. Key words: covolume method, rotated bilinear finite element method, duality, optimal order.

• Type: Journal
• Year: 2008
• Where: AMC
• Authors: Yun K. Hyon, Ho J. Jang, Do Y. Kwak
• Keywords: AMC 2008, Diagonal Tensor, Finite Element, Order Elliptic Pdes