Nonconforming cell boundary element methods for elliptic problems on triangular mesh

The nonconforming cell boundary element (CBE) methods are proposed. The methods are designed in such a way that they enjoy the mass conservation at the element level and the normal component of fluxes at inter-element boundaries are continuous for unstructured triangular meshes. Normal flux continuity and the optimal order error estimates in a broken H¹ norm for the P₁ method are established, which are completion of authors' earlier works [Y. Jeon, D. Sheen, Analysis of a cell boundary element method, Adv. Comput. Math. 22 (3) (2005) 201–222; Y. Jeon, E.-J. Park, D. Sheen, A cell boundary element method for elliptic problems, Numer. Methods Partial Differential Equations 21 (3) (2005) 496–511]. Moreover, two second order methods (the and modified methods) and a multiscale CBE method are constructed and numerical experiments are performed. Numerical results show feasibility and effectiveness of the CBE methods.