有限要素解析におけるソース項の保存型離散化（六面体要素の場合）
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概要
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The conventional Galerkin finite element solution is mesh dependent, and its discretization for Poisson's equation can not satisfy the conservation law at a nodal level when unstructured linear meshes are used. This research tries to solve these problems by introducing a new concept of the virtual nodal domain(Vnd) for a linear hexahedral element, and distributing the source term to a nodal algebraic equation in proportion to the volume of the Vnd. The Vnd is evaluated using a second-order flux existing within a linear element. We proved that the total Vnd of the eight nodes equals to the volume of the element, which guarantees that our scheme is also elementally conservative. Numerical simulation of heat conduction with both Dirichlet and Neumann boundary conditions shows that the accuracy has been improved obviously comparing with the conventional Galerkin FEM for unstructured hexahedral meshes, especially for bad quality elements. Our scheme can be introduced into any commercial FEM code quite easily.