On the conditioning of finite element equations with highly refined meshes
SIAM Journal on Numerical Analysis
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A Particle-Partition of Unity Method--Part III: A Multilevel Solver
SIAM Journal on Scientific Computing
A conforming finite element method for overlapping and nonmatching grids
Mathematics of Computation
Multilevel preconditioning for partition of unity methods: some analytic concepts
Numerische Mathematik
Superconvergence in the generalized finite element method
Numerische Mathematik
Journal of Computational and Applied Mathematics
Meshfree Particle Methods
Hi-index | 0.00 |
We study the asymptotic behavior of the condition number of the linear system from the discretization of a class of generalized finite element methods for solving second-order elliptic boundary value problems. Allowing local approximation spaces with polynomials of different degrees and different local patch sizes (local refinements), we give bounds on the condition number in relation to the patch size and the dimension of the global approximation space in which the shape functions are in general not polynomials. Numerical tests verify the theorems.