Nonconforming cell boundary element methods for elliptic problems on triangular mesh

Authors:
Youngmok Jeon;Eun-Jae Park
Affiliations:
Department of Mathematics, Ajou University, Suwon 443-749, Korea;Department of Mathematics, Yonsei University, Seoul, Korea
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

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 H^1 norm for the P"1 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 P"2^* and modified P"2^* methods) and a multiscale CBE method are constructed and numerical experiments are performed. Numerical results show feasibility and effectiveness of the CBE methods.