Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method

References

[1] T. Gyulov, G. Morosanu, On a class of boundary value problems involving the p-biharmonic operator, J. Math. Anal. Appl. 367 (2010), 43–57.10.1016/j.jmaa.2009.12.022Search in Google Scholar

[2] A. C. Lazer and P. J. Mckenna, Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Rev. 32 (1990), 537–578.10.1137/1032120Search in Google Scholar

[3] N. A. Golias and T. D. Tsiboukis, An approach to refining three-dimensional tetra-hedral meshes based on Delaunay transformations, Int. J. Numer. Methods Eng. 37 (1994), 793–812.10.1002/nme.1620370506Search in Google Scholar

[4] K. Höllig, U. Reif and J. Wipper, Weighted extended B-spline approximation of Dirichlet problems, SIAM J. Numer. Anal. 39 (2001), 442–462.10.1137/S0036142900373208Search in Google Scholar

[5] T. J. R. Hughes, J. A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng. 194 (2005), 4135–4195.10.1016/j.cma.2004.10.008Search in Google Scholar

[6] K. Höllig and J. Hörner, Programming finite element methods with weighted B-splines, Comput. Math. Appl. 70(7) (2015), 1441–1456.10.1016/j.camwa.2015.02.019Search in Google Scholar

[7] S. Chaudhary, V. Srivastava, V. V. K. Srinivas Kumar and B. Srinivasan, WEB-Spline based mesh-free finite element approximation for p-Laplacian, Int. J. Comput. Math. 93(6) (2016), 1022–1043.10.1080/00207160.2015.1016923Search in Google Scholar

[8] N. Rajashekar, S. Chaudhary and V. V. K. Srinivas Kumar, Minimization techniques for p(x)-Laplacian problem using WEB-Spline based mesh-free method, Int. J. Comput. Math. (2019), doi: 10.1080/00207160.2019.1585824.Search in Google Scholar

[9] L. M. Del Pezzo and S. MartÃnez, Order of convergence of the finite element method for the p(x)-Laplacian, IMA J. Numer. Anal. 35(4) (2015), 1864–1887.10.1093/imanum/dru050Search in Google Scholar

[10] W. B. Liu and J. W. Barrett, Finite element approximation of the p-Laplacian, Math. Comp. 61 (1993), 523–537.10.1090/S0025-5718-1993-1192966-4Search in Google Scholar

[11] E. Süli and I. Mozolevski, hp-version interior penalty DGFEMs for the biharmonic equation, Comput. Methods Appl. Mech. Eng. 196 (2007), 1851–1863.10.1016/j.cma.2006.06.014Search in Google Scholar

[12] R. K. Mohanty, W. Dai and F. Han, A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: Application to Navier–Stokes equations of motion, Int. J. Comput. Math. 92 (2015), 1574–1590.10.1080/00207160.2014.949251Search in Google Scholar

[13] R. K. Mohanty, McKee Sean and D. Kaur, A class of two-level implicit unconditionally stable methods for a fourth order parabolic equation, Appl. Math. Comput. 309 (2017), 272–280.10.1016/j.amc.2017.04.009Search in Google Scholar

[14] N. Katzourakis and T. Pryer, On the numerical approximation of p-biharmonic and ∞ -biharmonic functions, Numer. Methods Partial Differ. Eq. 35(1) (2019), 155–180.10.1002/num.22295Search in Google Scholar

[15] T. Pryer, Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective, Electron. Trans. Numer. Anal. 41 (2014), 328–349.Search in Google Scholar

[16] A. Streit, Finite elemente approximation der Plattengleichung mit web-Splines. Universität Stuttgart, Diplomarbeit, 2002.Search in Google Scholar

[17] K. Höllig, Finite element methods with B-splines, SIAM, Philadelphia, 2003.10.1137/1.9780898717532Search in Google Scholar

[18] M. G. Cox, The numerical evaluation of B-Splines, J. Inst. Math. Appl. 10 (1972), 134–149.10.1093/imamat/10.2.134Search in Google Scholar

[19] C. de Boor, On calculating with B-Splines, J. Approx. Theory 6 (1972), 50–62.10.1016/0021-9045(72)90080-9Search in Google Scholar

[20] L. W. Kantorowitsch and W. I. Krylow, Näherungsmethoden der Höheren analysis, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956.Search in Google Scholar

[21] V. L. Rvachev and T. I. Sheiko, R-functions in boundary value problems in mechanics, Appl. Mech. Rev. 48 (1995), 151–188.10.1115/1.3005099Search in Google Scholar

[22] P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, 1978.10.1115/1.3424474Search in Google Scholar

[23] M. Caliari and S. Zuccher, Quasi-Newton minimization for the p(x)-Laplacian problem, J. Comput. Appl. Math. 309 (2017), 122–131.10.1016/j.cam.2016.06.026Search in Google Scholar

[24] G. Zhou, Y. Huang and C. Feng, Preconditioned hybrid conjugate gradient algorithm for p-Laplacian, Int. J. Numer. Anal. Model. 2 (2005), 123–130.Search in Google Scholar