Abstract
The conventional Galerkin FEM sometimes can not converge on, for example, the original Poisson's equation locally when unstructured linear meshes are used. This problem arises from the inconsistency from the viewpoint of conservation law between the discretization of the source team and one of other terms. This research tries to solve this problem by distributing the source term to nodal algebraic equations in proportion to the areas of nodal domains. The nodal domains are introduced using second-order fluxes. Only the source distribution within an element is counted even for an obtuse triangle, which reduces numerical error effectively where the source term changes spatially. Numerical simulation of heat conduction with both Dirichlet and Neumann boundary conditions shows that the numerical accuracy has been improved obviously comparing with the conventional Galerkin FEM for unstructured triangular meshes, especially for bad quality elements.
