Haoze He,Daniel Kressner
Haoze He
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A. ...
Nis-Erik Bohne,Benedikt Gräßle,Stefan A Sauter
Nis-Erik Bohne
The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximations. However, it is well known that the convergence rates for...
On the convergence rate of the Kačanov scheme for shear-thinning fluids [0.03%]
Kacanov方案求解剪切稀化流体收敛率分析
Pascal Heid,Endre Süli
Pascal Heid
We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contract...
All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations [0.03%]
一类求解一维空间分数阶扩散方程的整体多重网格方法
Marco Donatelli,Rolf Krause,Mariarosa Mazza et al.
Marco Donatelli et al.
We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields...
Approximating inverse FEM matrices on non-uniform meshes with [Formula: see text] -matrices [0.03%]
非均匀网格上用[公式请参见文本] -矩阵近似逆FEM矩阵
Niklas Angleitner,Markus Faustmann,Jens Markus Melenk
Niklas Angleitner
We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse H -matrix format. For a large class of shape regular but possibly non-uniform meshes including algebraically graded meshes, we prove that...
Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces [0.03%]
求解曲面上椭圆方程的任意阶本征虚拟元方法
Elena Bachini,Gianmarco Manzini,Mario Putti
Elena Bachini
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covari...
[Formula: see text] -conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes [0.03%]
笛卡尔网格上的[公式：见文本]-协调有限元链复合体及交换拟插值算子
Francesca Bonizzoni,Guido Kanschat
Francesca Bonizzoni
A finite element cochain complex on Cartesian meshes of any dimension based on the H 1 -inner product is introduced. It yields H 1 -conforming finite element spaces with exterior derivatives in H 1 . We use a tensor product construction ...