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Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs
dc.contributor.author | Surana, Karan S. | |
dc.contributor.author | Euler, L. | |
dc.contributor.author | Reddy, J. N. | |
dc.contributor.author | Romkes, A. | |
dc.date.accessioned | 2015-11-10T16:13:22Z | |
dc.date.available | 2015-11-10T16:13:22Z | |
dc.date.issued | 2011-06 | |
dc.identifier.citation | Surana, K.s., L. Euler, J.n. Reddy, and A. Romkes. "Methods of Approximation in Hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs." American Journal of Computational Mathematics AJCM 01.02 (2011): 83-103. http://dx.doi.org/10.4236/ajcm.2011.12009 | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/18871 | |
dc.description | This is the published version. Copyright © 2011 Scientific Research Publishing | en_US |
dc.description.abstract | The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak form (/GMWF ), Petrov-Galerkin method (PGM), weighted residual method (WRY ), and least squares method or process (LSM or LSP ) to construct finite element approximations in time. A correspondence is estab- lished between these integral forms and the elements of the calculus of variations: 1) to determine which methods of approximation yield unconditionally stable (variationally consistent integral forms, VC ) com- putational processes for which types of operators and, 2) to establish which integral forms do not yield un- conditionally stable computations (variationally inconsistent integral forms, VIC). It is shown that varia- tionally consistent time integral forms in hpk framework yield computational processes for ODEs in time that are unconditionally stable, provide a mechanism of higher order global differentiability approxima- tions as well as higher degree local approximations in time, provide control over approximation error when used as a time marching process and can indeed yield time accurate solutions of the evolution. Numerical studies are presented using standard model problems from the literature and the results are compared with Wilson’s method as well as Newmark method to demonstrate highly meritorious features of the pro- posed methodology. | en_US |
dc.publisher | Scientific Research Publishing | en_US |
dc.subject | Finite Element Approximations | en_US |
dc.subject | Numerical Studies | en_US |
dc.subject | Time Approximation | en_US |
dc.subject | Variationally Consistent Integral Forms | en_US |
dc.title | Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs | en_US |
dc.type | Article | |
kusw.kuauthor | Surana, Karan S. | |
kusw.kudepartment | Mechanical Engineering | en_US |
dc.identifier.doi | 10.4236/ajcm.2011.12009 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |