کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
521201 | 867758 | 2008 | 20 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids](/preview/png/521201.png)
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer’s vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer’s. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer’s method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Journal: Journal of Computational Physics - Volume 227, Issue 8, 1 April 2008, Pages 3738–3757