Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor...Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.展开更多
We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplaci...We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplacian with the inhomogeneous Dirichlet boundary condition and give the corresponding truncation errors with the help of the interpolation estimate.Moreover,the suitable corrections are proposed to guarantee the convergence in solving the inhomogeneous fractional Dirichlet problem and an O(h^(1+α)2s))convergence rate is obtained when the solution u∈C^(1,α)(Ω_(n)^(δ)),where n is the dimension of the space,∈(max(0,2s−1),1],δis a fixed positive constant,and h denotes mesh size.Finally,the performed numerical experiments confirm the theoretical results.展开更多
文摘Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.
基金supported by the National Natural Science Foundation of China(Grant No.12071195)the AI and Big Data Funds(Grant No.2019620005000775)+1 种基金by the Fundamental Research Funds for the Central Universities(Grant Nos.lzujbky-2021-it26,lzujbky-2021-kb15)NSF of Gansu(Grant No.21JR7RA537).
文摘We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplacian with the inhomogeneous Dirichlet boundary condition and give the corresponding truncation errors with the help of the interpolation estimate.Moreover,the suitable corrections are proposed to guarantee the convergence in solving the inhomogeneous fractional Dirichlet problem and an O(h^(1+α)2s))convergence rate is obtained when the solution u∈C^(1,α)(Ω_(n)^(δ)),where n is the dimension of the space,∈(max(0,2s−1),1],δis a fixed positive constant,and h denotes mesh size.Finally,the performed numerical experiments confirm the theoretical results.
