Mass lumping models of the linear diffusion equation |
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| Authors: | TV Hromadka GL Guymon |
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| Institution: | Department of Civil Engineering, University of California, Irvine, California 92717, USA;Department of Civil Engineering, University of California, Irvine, California 92717, USA |
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| Abstract: | The nodal domain integration method is used to develop a numerical model of the linear diffusion equation. The nodal domain integration approach is shown to represent an infinity of finite element mass matrix lumping schemes including the Galerkin and subdomain integration versions of the weighted residual method and an integrated finite difference method. Neumann, Dirichlet and mixed boundary conditions are accommodated analogous to the Galerkin finite element method. In order to reduce the overall integrated approximation relative error, a mass matrix lumping formulation is developed which is based on the Crank-Nicolson time advancement approximation. The optimum mass lumping factors are found to be strongly related to the model timestep size. |
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