On the conditioning of finite element equations with highly refined meshes
SIAM Journal on Numerical Analysis
Efficient preconditioning for the p-version finite element method in two dimensions
SIAM Journal on Numerical Analysis
Timely Communication: Diagonal Edge Preconditioners in p-version and Spectral Element Methods
SIAM Journal on Scientific Computing
Bounds for eigenvalues and condition numbers in the p-version of the finite element method
Mathematics of Computation
Spectral element methods on triangles and quadrilaterals: comparisons and applications
Journal of Computational Physics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Finite-Element Preconditioning of G-NI Spectral Methods
SIAM Journal on Scientific Computing
| Hi-index | 7.30 |
Sharp bounds on the condition number of stiffness matrices arising in hp/spectral discretizations for two-dimensional problems elliptic problems are given. Two types of shape functions that are based on Lagrange interpolation polynomials in the Gauss-Lobatto points are considered. These shape functions result in condition numbers O(p) and O(p ln p) for the condensed stiffness matrices, where p is the polynomial degree employed. Locally refined meshes are analyzed. For the discretization of Dirichlet problems on meshes that are refined geometrically toward singularities, the conditioning of the stiffness matrix is shown to be independent of the number of layers of geometric refinement.