%0 Report %1 citeulike:13441833 %A Babuska, I. %A Craig, A. %A Mandel, J. %A Pitkäranta, J. %C College Park, MD %D 1989 %K 65y05-parallel-computation 65f08-preconditioners-for-iterative-methods 65n30-pdes-bvps-finite-elements 65n55-pdes-bvps-multigrid-methods-domain-decomposition %N BN-1105 %R 10.1137/0728034 %T Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions %U http://dx.doi.org/10.1137/0728034 %X We formulate and analyze parallel preconditioners for systems of equations arising from the \$p\$-version finite element method. Using new theoretical results for polynomial spaces, we prove that condition number grows as \$łog^2 p\$, where \$p\$ is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with \$p\$.

@techreport{citeulike:13441833, abstract = {{We formulate and analyze parallel preconditioners for systems of equations arising from the \$p\$-version finite element method. Using new theoretical results for polynomial spaces, we prove that condition number grows as \$\log^2 p\$, where \$p\$ is the degree of the polynomial space. Numerical results are presented showing that the condition number indeed grows very slowly with \$p\$.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {College Park, MD}, author = {Babu\v{s}ka, I. and Craig, A. and Mandel, J. and Pitk\"{a}ranta, J.}, biburl = {https://www.bibsonomy.org/bibtex/2c268f57e6a9c807518027ddd096f06e1/gdmcbain}, citeulike-article-id = {13441833}, citeulike-linkout-0 = {http://dx.doi.org/10.1137/0728034}, doi = {10.1137/0728034}, institution = {Institute for Physical Science and Technology, Universityof Maryland}, interhash = {fec170413e7de0b526852d9143a4b9a2}, intrahash = {c268f57e6a9c807518027ddd096f06e1}, keywords = {65y05-parallel-computation 65f08-preconditioners-for-iterative-methods 65n30-pdes-bvps-finite-elements 65n55-pdes-bvps-multigrid-methods-domain-decomposition}, month = oct, number = {BN-1105}, posted-at = {2014-11-24 00:19:53}, priority = {2}, timestamp = {2019-02-28T23:46:00.000+0100}, title = {{Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions}}, url = {http://dx.doi.org/10.1137/0728034}, year = 1989 }