TY - JOUR
T1 - Explicit Bounds of Eigenvalues for Stiffness Matrices by Quadratic Hierarchical Basis Method
AU -  Sang Dong Kim & Byeong Chun Shin 
JO - Journal of Computational Mathematics
VL - 2
SP - 113
EP - 124
PY - 2003
DA - 2003/04
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8874.html
KW - hierarchical basis, multilevel.
AB - <p style="text-align: justify;">The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to $Lu := - u&#39;&#39; $ with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like $O(\frac{1}{h})$ where $h$ is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to $O(1)$.</p>