FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2014445341> ?p ?o ?g. }

• W2014445341 endingPage "207" @default.
• W2014445341 startingPage "133" @default.
• W2014445341 abstract "International Journal of Computational Engineering ScienceVol. 05, No. 01, pp. 133-207 (2004) No AccessTHE K-VERSION OF FINITE ELEMENT METHOD FOR NONLINEAR OPERATORS IN BVPK. S. SURANA, A. R. AHMADI, and J. N. REDDYK. S. SURANADepartment of Mechanical Engineering, University of Kansas, Lawrence, KS 66044, USA Search for more papers by this author , A. R. AHMADIDepartment of Mechanical Engineering, University of Kansas, Lawrence, KS 66044, USA Search for more papers by this author , and J. N. REDDYDepartment of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA Search for more papers by this author https://doi.org/10.1142/S1465876304002307Cited by:29 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIn the companion papers [1,2], authors introduced the concepts of k-version of finite element method and k, hk, pk, hkp-processes of the finite element method for boundary value problems described by self-adjoint and non-self adjoint operators using Ĥk,p(Ω) spaces with specific details including numerical studies for weak forms and least square processes. It was demonstrated that a variationally consistent (VC) weak form is possible when the differential operator is self-adjoint, however, in case of non-self-adjoint operators the weak forms are variationally inconsistent (VIC) which lead to degenerate computational processes that can produce spurious oscillations in the computed solutions. In this paper we demonstrate that when the boundary value problems are described by non-linear differential operators, Galerkin processes and weak forms can never be variationally consistent and hence result in degenerate computational processes and suffer from same problems as in the case of non-self-adjoint operators plus more due to the presence of non-linearity. In the proposed mathematical and computational frame-work, upwinding methods are neither required nor used. The k-version of FEM over Ĥk,p spaces for the Galerkin method with weak forms, though meritorious in comparison to Ĥ1,p(Ω) spaces, but it is plagued due to problems arising from variational inconsistency.We demonstrate that the order of the space k in Ĥk,p(Ω) Hilbert spaces is an independent parameter in all computational processes in addition to the characteristic length h of the discretizations and the degree p of the local approximations. This gives rise to k-version of finite element method and thus, associated k, hk, pk, and hpk processes. The global differentiability of a finite element solution is only dependent on k. The h, p and hp-adaptive processes can not yield global differentiability of order higher than the order of the space containing the local approximations. It is shown that variational consistency of the integral forms and higher order global differentiability of a computed solution by increasing k in Ĥk,p(Ω) spaces are two most important features of mathematical and computational frame work if one wishes the computational process to (1) be non-degenerate and (2) yield solution with the same characteristics in terms of global differentiability as the theoretical solution.In this paper, we illustrate the important variational aspects of the least squares finite element processes for non-linear partial differential equations of stationary processes. Variationally consistent least squares finite element method (LSFEM) using p-version basis functions in Ĥk,p(Ω) spaces provides a remarkably general framework for numerical simulation of any BVP described by non-linear differential operators in which any desired order of global smoothness or global differentiability is achievable. The proposed mathematical framework indeed allows one to numerically simulate characteristics of the theoretical solutions of any non-linear BVP regardless of the nature of the differential operator. Stationary one-dimensional Burgers equation is used as a model problem to present supporting numerical studies. Many issues and concepts related to upwinding methods and the behaviors of commonly encountered problems in Galerkin method for non-linear differential operators in BVP are considered, discussed and explained. References K. S. Surana, A. R. Ahmadi and J. N. Reddy, Int. J. Comp. Engng. Sci. 3(2), 155 (2002). Link, Google Scholar Surana, K. S., Ahmadi, A. R., and Reddy, J. N., k-version of finite element method in Ĥk,p spaces for non-self-adjoint operators in boundary value problems, Int. J. Comp. Engng. Sci., to appear . Google Scholar G. F. Carey and J. T. Oden , Finite Elements: A Second Course II ( Prentice Hall , Englewood Cliffs, N.J. , 1983 ) . Google Scholar J. T. Oden and G. F. Carey , Finite Elements: Mathematical Aspects ( Prentice Hall , Englewood Cliffs, N.J. , 1983 ) . Google Scholar C. Johnson , Numerical Solution of Partial Differential Equations by Finite Element Method ( Cambridge University Press , 1987 ) . Google Scholar B. A. Finlayson , Numerical Methods for Problems with Moving Fronts ( Ravema Park Publishing Company, Seattle , Washington , 1992 ) . Google ScholarT. J. R. Hughes, Int. J. Num. Meth. Eng. 12, 1359 (1978). Crossref, Google ScholarA. N. Brooks and T. J. R. Hughes, Comp. Meth. Appl. Mech. Engrg. 32, 199 (1982). Crossref, Google ScholarT. J. R. Hughes and M. A. Mallet, Comp. Meth. Appl. Mech. Engrg. 58, 305 (1986). Crossref, Google ScholarT. J. R. Hughes and M. Mallet, Computer Methods in Applied Mechanics and Engineering 58, 329 (1986). Crossref, Google ScholarT. J. R. Hughes, M. Mallet and A. Mizukami, Comp. Meth. Appl. Mech. Engrg. 54, 341 (1986). Crossref, Google ScholarG. L. LeBeau and T. E. Tezduyar, Advances in Finite Element Analysis in Fluid Dynamics 123 (1991) pp. 21–27. Google ScholarF. Shakib, T. J. R. Hughes and Z. Johan, Comp. Meth. Appl. Mech. Engrg. 89, 141 (1991). Crossref, Google ScholarL. P. Franca, S. L. Frey and T. J. R. Hughes, Computer Methods in Applied Mechanics and Engineering 95, 253 (1992). Crossref, Google ScholarI. Christieet al., Int. J. Num. Meth. Engrg. 10, 1389 (1976). Crossref, Google ScholarJ. C. Hienrich, P. S. Huyakorn and O. C. Zienkiewicz, Int. J. Num. Meth. Engrg. 11, 131 (1977). Crossref, Google ScholarJ. C. Hienrich and O. C. Zienkiewicz, Int. J. Num. Meth. Engrg. 11, 1831 (1977). Crossref, Google ScholarJ. C. Hienrich, Int. J. Num. Meth. Engrg. 15, 1041 (1980). Crossref, Google ScholarD. W. Kellyet al., Int. J. Num. Meth. Engrg. 15, 1705 (1980). Crossref, Google Scholar Winterscheidt, D., p-version least squares finite element methods for fluid dynamics, Ph.D. Thesis, University of Kansas, 1992 . Google Scholar Van Dyne, D. G., Non-weak/strong Solutions in Gas Dynamics, Ph.D. Thesis, University of Kansas, 1999 . Google ScholarP. P. Lynn and K. Alani, Int. J. Num. Meth. Engrg. 10, 809 (1976). Crossref, Google ScholarJ. F. Polk and P. P. Lynn, Int. J. Num. Meth. Engrg. 12, 3 (1978). Google Scholar Jiang, B. N., Least-square finite element methods with element-by-element solution including adaptive refinement, Ph.D. Dissertation, University of Texas at Austin, 1986 . Google ScholarB. N. Jiang and C. F. Carey, Int. J. Num. Meth. Fluids 8, 933 (1988). Crossref, Google ScholarI. Kececioglu and B. Rubinsky, Int. J. Num. Meth. Engrg. 28, 2583 (1989). Crossref, Google ScholarI. Kececioglu and B. Rubinsky, Int. J. Num. Meth. Engrg. 28, 2609 (1989). Crossref, Google ScholarI. Kececioglu and B. Rubinsky, Int. J. Num. Meth. Engrg. 28, 2715 (1989). Crossref, Google ScholarC. L. Chang and B. N. Jiang, Comp. Meth. Appl. Mech. Engrg. 84, 247 (1980). Crossref, Google ScholarB. N. Jiang and L. A. Povinelli, Comp. Meth. Appl. Mech. Engrg. 81, 13 (1980). Crossref, Google ScholarD. Wintershiedt and K. S. Surana, Int. J. Num. Meth. Engrg. 36, 3629 (1993). Crossref, Google ScholarD. Wintershiedt and K. S. Surana, Int. J. Num. Meth. Engrg. 18, 43 (1994). Crossref, Google ScholarD. Wintershiedt and K. S. Surana, Int. J. Num. Meth. Engrg. 36, 111 (1993). Crossref, Google ScholarB. C. Bell and K. S. Surana, Int. J. Num. Meth. Engrg. 18, 127 (1993). Crossref, Google Scholar Bell, B. C., and Surana, K. S., p-version space-time coupled least squares finite element formulation for two dimensional unsteady incompressible Newtonian fluid flow, Presented at 1993 ASME Winter Annual Meeting, 1993 . Google ScholarB. C. Bell and K. S. Surana, Int. J. Num. Meth. Engrg. 37, 3545 (1994). Crossref, Google ScholarB. C. Bell and K. S. Surana, Int. J. Num. Meth. Engrg. 39, 2593 (1996). Crossref, Google ScholarN. B. Edgar and K. S. Surana, Comp. Meth. Appl. Mech. Engrg. 113, 271 (1994). Crossref, Google ScholarK. S. Surana and J. S. Sandhu, Comp. Mech. 16, 151 (1995). Crossref, Google ScholarK. S. Surana and M. Bona, Int. J. Computational Engg. Sci. 1(2), 299 (2000). Link, Google ScholarK. S. Surana and David G. Van Dyne, Int. J. Num. Meth. Engrg. 53, 1051 (2002). Crossref, Google ScholarK. S. Surana and David G. Van Dyne, Int. J. Comp. Engg. Sci. (2002). Google ScholarK. S. Surana and David G. Van Dyne, Int. J. Num. Meth. Engrg. 53, 1025 (2002). Crossref, Google ScholarK. S. Surana and David G. , Int. J. Num. Meth. Engrg. (2001). Google ScholarK. S. Suranaet al., Int. J. Comp. Eng. Sci. (2002). Google Scholar I. M. Gelfand and S. V. Fomin , Calculus of Variations ( Dover Publications , New York , 2000 ) . Google Scholar FiguresReferencesRelatedDetailsCited By 29A Thermodynamically Consistent Formulation for Dynamic Response of Thermoviscoelastic Plate/Shell Based on Classical Continuum Mechanics (CCM)K. S. Surana and S. S. C. Mathi31 December 2020 | International Journal of Structural Stability and Dynamics, Vol. 20, No. 14Highly accurate space-time coupled least-squares finite element framework in studying wave propagationM. A. Saffarian, A. R. Ahmadi and M. H. Bagheripour16 March 2020 | SN Applied Sciences, Vol. 2, No. 4Finite Element Processes Based on GM/WF in Non-Classical Solid MechanicsK. S. Surana, R. Shanbhag and J. N. Reddy1 Jan 2017 | American Journal of Computational Mathematics, Vol. 07, No. 03Non-Linear Differential OperatorsKaran S. Surana and J. N. Reddy17 Nov 2016Error Estimations, Error Computations, and Convergence Rates in FEM for BVPsKaran S. Surana, A. D. Joy and J. N. Reddy1 Jan 2016 | Applied Mathematics, Vol. 07, No. 12Nonlinear Waves in Solid Continua with Finite DeformationK. S. Surana, J. Knight and J. N. Reddy1 Jan 2015 | American Journal of Computational Mathematics, Vol. 05, No. 03Mathematical models for fluid–solid interaction and their numerical solutionsK.S. Surana, B. Blackwell, M. Powell and J.N. Reddy1 Oct 2014 | Journal of Fluids and Structures, Vol. 50Riemann shock tube: 1D normal shocks in air, simulations and experimentsK.S. Surana, K.P.J. Reddy, A.D. Joy and J.N. Reddy12 June 2014 | International Journal of Computational Fluid Dynamics, Vol. 28, No. 6-10Ordered rate constitutive theories in Lagrangian description for thermoviscoelastic solids without memoryK. S. Surana, T. Moody and J. N. Reddy4 June 2013 | Acta Mechanica, Vol. 224, No. 11Static deflection analysis of flexural rectangular micro-plate using higher continuity finite-element methodAli Reza Ahmadi and Hamed Farahmand6 November 2012 | Mechanics & Industry, Vol. 13, No. 4Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPsK.S. Surana, L. Euler, J.N. Reddy and A. Romkes1 Jan 2011 | American Journal of Computational Mathematics, Vol. 01, No. 02The Rate Constitutive Equations and Their Validity for Progressively Increasing DeformationKaran S. Surana, Yongting Ma, Albert Romkes and J. N. Reddy19 Oct 2010 | Mechanics of Advanced Materials and Structures, Vol. 17, No. 7Computations of Numerical Solutions in Polymer Flows Using Giesekus Constitutive Model in the hpk Framework with Variationally Consistent Integral FormsKaran S. Surana, Kedar M. Deshpande, Albert Romkes and J. N. Reddy13 Aug 2009 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 10, No. 5J-Integral for Mode I Linear Elastic Fracture Mechanics in h, p, k Mathematical and Computational FrameworkD. Nunez, K. S. Surana, A. Romkes and J. N. Reddy13 Aug 2009 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 10, No. 5Numerical Simulations of BVPs and IVPs in Fiber Spinning Using Giesekus Constitutive Model in hpk FrameworkKaran S. Surana, Kedar M. Deshpande, Albert Romkes and J. N. Reddy10 Mar 2009 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 10, No. 2Numerical Solutions of BVPs in 2-D Viscous Compressible Flows Using hpk FrameworkS. Allu, K. S. Surana, A. Romkes and J. N. Reddy10 Mar 2009 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 10, No. 2Higher Order Global Differentiability Local Approximations for 2-D Distorted Quadrilateral ElementsA. Ahmadi, K. S. Surana, R. K. Maduri, A. Romkes and J. N. Reddy12 Feb 2009 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 10, No. 1k-Version of finite element method in 2D-polymer flows: Upper convected Maxwell modelK.S. Surana, S. Bhola, J.N. Reddy and P.W. TenPas1 Sep 2008 | Computers & Structures, Vol. 86, No. 17-18Least‐squares finite element processes in h, p, k mathematical and computational framework for a non‐linear conservation lawK. S. Surana, S. Allu, J. N. Reddy and P. W. Tenpas10 Aug 2008 | International Journal for Numerical Methods in Fluids, Vol. 57, No. 10Strong and Weak Form of the Governing Differential Equations in Least Squares Finite Element Processes in h,p,k FrameworkK. S. Surana, L. R. Anthoni, S. Allu and J. N. Reddy1 Jan 2008 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 9, No. 1Galerkin/Least-Squares Finite Element Processes for BVP in h, p, k Mathematical FrameworkK. S. Surana, R. Kanti Mahanthi and J. N. Reddy5 Oct 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 8, No. 6Galerkin and Least-Squares Finite Element Processes for 2-D Helmholtz Equation in h , p , k FrameworkK. S. Surana, P. Gupta and J. N. Reddy31 Jul 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 8, No. 5k -Version Least Squares Finite Element Processes for 2-D Generalized Newtonian Fluid FlowsK. S. Surana, M. K. Engelkemier, J. N. Reddy and P. W. Tenpas22 May 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 8, No. 4The k-Version of Finite Element Method for Initial Value Problems: Mathematical and Computational FrameworkK. S. Surana, J. N. Reddy and S. Allu10 April 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 8, No. 3k-version of finite element method in gas dynamics: higher-order global differentiability numerical solutionsK. S. Surana, S. Allu, P. W. Tenpas and J. N. Reddy1 January 2007 | International Journal for Numerical Methods in Engineering, Vol. 69, No. 6k-Version of finite element method in 2-D polymer flows: Oldroyd-B constitutive modelK. S. Surana, A. Mohammed, J. N. Reddy and P. W. TenPas1 January 2006 | International Journal for Numerical Methods in Fluids, Vol. 52, No. 2h, p, k Least Squares Finite Element Processes for 1-D Helmholtz EquationK. S. Surana, P. Gupta, P. W. Tenpas and J. N. Reddy23 February 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 7, No. 4The k -Version Finite Element Method for Singular Boundary-Value Problems with Application to Linear Fracture MechanicsK. S. Surana, A. Rajwani and J. N. Reddy23 February 2007 | International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 7, No. 3Elastic Wave Propagation in Laminated Composites Using the Space-Time Least-Squares Formulation in h,p,k FrameworkK. S. Surana, R. K. Maduri, P. W. TenPas and J. N. Reddy1 Mar 2006 | Mechanics of Advanced Materials and Structures, Vol. 13, No. 2 Recommended Vol. 05, No. 01 Metrics History PDF download" @default.
• W2014445341 created "2016-06-24" @default.
• W2014445341 creator A5016498640 @default.
• W2014445341 creator A5053596832 @default.
• W2014445341 creator A5067765504 @default.
• W2014445341 date "2004-03-01" @default.
• W2014445341 modified "2023-10-14" @default.
• W2014445341 title "THE K-VERSION OF FINITE ELEMENT METHOD FOR NONLINEAR OPERATORS IN BVP" @default.
• W2014445341 cites W1992073061 @default.
• W2014445341 cites W1994125095 @default.
• W2014445341 cites W1994275329 @default.
• W2014445341 cites W2010468148 @default.
• W2014445341 cites W2011911051 @default.
• W2014445341 cites W2015274185 @default.
• W2014445341 cites W2026039582 @default.
• W2014445341 cites W2037160381 @default.
• W2014445341 cites W2045793197 @default.
• W2014445341 cites W2065438814 @default.
• W2014445341 cites W2066090268 @default.
• W2014445341 cites W2067099342 @default.
• W2014445341 cites W2073897969 @default.
• W2014445341 cites W2081177856 @default.
• W2014445341 cites W2081384586 @default.
• W2014445341 cites W2085108570 @default.
• W2014445341 cites W2091893176 @default.
• W2014445341 cites W2092594135 @default.
• W2014445341 cites W2093322335 @default.
• W2014445341 cites W2095327521 @default.
• W2014445341 cites W2102211172 @default.
• W2014445341 cites W2108867814 @default.
• W2014445341 cites W2115855800 @default.
• W2014445341 cites W2127473876 @default.
• W2014445341 cites W2127567312 @default.
• W2014445341 cites W2137161281 @default.
• W2014445341 cites W2144502017 @default.
• W2014445341 cites W2146049526 @default.
• W2014445341 cites W2157542012 @default.
• W2014445341 cites W2163201983 @default.
• W2014445341 cites W4235380276 @default.
• W2014445341 doi "https://doi.org/10.1142/s1465876304002307" @default.
• W2014445341 hasPublicationYear "2004" @default.
• W2014445341 type Work @default.
• W2014445341 sameAs 2014445341 @default.
• W2014445341 citedByCount "31" @default.
• W2014445341 countsByYear W20144453412012 @default.
• W2014445341 countsByYear W20144453412013 @default.
• W2014445341 countsByYear W20144453412014 @default.
• W2014445341 countsByYear W20144453412015 @default.
• W2014445341 countsByYear W20144453412016 @default.
• W2014445341 countsByYear W20144453412017 @default.
• W2014445341 countsByYear W20144453412020 @default.
• W2014445341 crossrefType "journal-article" @default.
• W2014445341 hasAuthorship W2014445341A5016498640 @default.
• W2014445341 hasAuthorship W2014445341A5053596832 @default.
• W2014445341 hasAuthorship W2014445341A5067765504 @default.
• W2014445341 hasConcept C121332964 @default.
• W2014445341 hasConcept C135628077 @default.
• W2014445341 hasConcept C136119220 @default.
• W2014445341 hasConcept C158622935 @default.
• W2014445341 hasConcept C202444582 @default.
• W2014445341 hasConcept C28826006 @default.
• W2014445341 hasConcept C33923547 @default.
• W2014445341 hasConcept C62520636 @default.
• W2014445341 hasConcept C97355855 @default.
• W2014445341 hasConceptScore W2014445341C121332964 @default.
• W2014445341 hasConceptScore W2014445341C135628077 @default.
• W2014445341 hasConceptScore W2014445341C136119220 @default.
• W2014445341 hasConceptScore W2014445341C158622935 @default.
• W2014445341 hasConceptScore W2014445341C202444582 @default.
• W2014445341 hasConceptScore W2014445341C28826006 @default.
• W2014445341 hasConceptScore W2014445341C33923547 @default.
• W2014445341 hasConceptScore W2014445341C62520636 @default.
• W2014445341 hasConceptScore W2014445341C97355855 @default.
• W2014445341 hasIssue "01" @default.
• W2014445341 hasLocation W20144453411 @default.
• W2014445341 hasOpenAccess W2014445341 @default.
• W2014445341 hasPrimaryLocation W20144453411 @default.
• W2014445341 hasRelatedWork W1557945163 @default.
• W2014445341 hasRelatedWork W1985218657 @default.
• W2014445341 hasRelatedWork W1989920940 @default.
• W2014445341 hasRelatedWork W2023661790 @default.
• W2014445341 hasRelatedWork W2096753949 @default.
• W2014445341 hasRelatedWork W2963341196 @default.
• W2014445341 hasRelatedWork W3106133691 @default.
• W2014445341 hasRelatedWork W3124205579 @default.
• W2014445341 hasRelatedWork W4249580765 @default.
• W2014445341 hasRelatedWork W608796411 @default.
• W2014445341 hasVolume "05" @default.
• W2014445341 isParatext "false" @default.
• W2014445341 isRetracted "false" @default.
• W2014445341 magId "2014445341" @default.
• W2014445341 workType "article" @default.