A least squares based diamond scheme for anisotropic diffusion problems
on polygonal meshes
- cheng dong,
- Tong Kang
cheng dong
Communication University of China School of Information and Communication Engineering
Author ProfileAbstract
We present a new least squares based diamond scheme for anisotropic
diffusion problems on polygonal meshes. This scheme introduces both
cell-centered unknowns and vertexunknowns. The vertex unknowns are
intermediate ones and are expressed aslinear combinations with the
surrounding cell-centeredunknowns by a new vertex interpolation
algorithm which is alsoderived in least squares approach. The least
squares approach is very flexible due to that theleast squares method
can solve overdetermined linear system. Both of the new scheme and the
vertex interpolation algorithmare applicable to diffusion problems with
discontinuous andanisotropic diffusion tensor on polygonal meshes.
Besides, they are linearity-preserving under givenassumptions, and the
optimal converge rates for both L2 errorand H1 error are observed in
numerical experiments. More interesting is that a very robust
performance of the newvertex interpolation algorithm on random meshes
compared withthe algorithm LPEW2 can be found from the numerical tests.