IS 2K-CONJECTURE VALID FOR FINITE VOLUME METHODS?

作者：Cao, Waixiang; Zhang, Zhimin; Zou, Qingsong^*

来源：SIAM Journal on Numerical Analysis, 2015, 53(2): 942-962.

DOI：10.1137/130936178

• superconvergence
• finite volume method
• 2k-conjecture

This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove the 2k-conjecture: at each vertex of the underlying rectangular mesh, the bi-k degree finite volume solution approximates the exact solution with an order O(h(2k)), where h is the mesh size. As byproducts, superconvergence properties for finite volume discretization errors at Lobatto and Gauss points are also obtained. All theoretical findings are confirmed by numerical experiments.

• 出版日期2015
• 单位北京计算科学研究中心; 中山大学