MOVCOL4: A moving mesh code for fourth-order time-dependent partial differential equations We develop and analyze a moving mesh code for the adaptive simulation of fourth-order PDEs based on collocation. The scheme is shown to enforce discrete conservation for problems written in a generalized conservation form. To demonstrate the breadth of applicability we present examples from both Cahn-Hilliard and thin-film -- type equations exhibiting metastable behavior, finite-time solution blow-up, finite-time extinction, and moving interfaces.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. DiPietro, Kelsey L.; Lindsay, Alan E.: Adaptive solution to two-dimensional partial differential equations in curved domains using the Monge-Ampére equation (2019)
  2. DiPietro, Kelsey L.; Haynes, Ronald D.; Huang, Weizhang; Lindsay, Alan E.; Yu, Yufei: Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems (2018)
  3. DiPietro, Kelsey L.; Lindsay, Alan E.: Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems (2017)
  4. Foster, Erich L.; Lohéac, Jérôme; Tran, Minh-Binh: A structure preserving scheme for the Kolmogorov-Fokker-Planck equation (2017)
  5. Zhou, Zhiqiang; Wu, Xiaodan: Simulation of blow-up solutions to the generalized KdV equations by moving collocation methods (2016)
  6. Lindsay, Alan E.: An asymptotic study of blow up multiplicity in fourth order parabolic partial differential equations (2014)
  7. Lu, Changna; Huang, Weizhang; Van Vleck, Erik S.: The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations (2013)
  8. Hazel, Andrew L.; Heil, Matthias; Waters, Sarah L.; Oliver, James M.: On the liquid lining in fluid-conveying curved tubes (2012)
  9. Lindsay, A. E.; Lega, J.: Multiple quenching solutions of a fourth order parabolic PDE with a singular nonlinearity modeling a MEMS capacitor (2012)
  10. Ma, Jingtang; Huang, Weizhang; Russell, Robert D.: Analysis of a moving collocation method for one-dimensional partial differential equations (2012)
  11. Ma, Jingtang; Jiang, Yingjun: Moving collocation methods for time fractional differential equations and simulation of blowup (2011)
  12. Budd, C. J.; Williams, J. F.: How to adaptively resolve evolutionary singularities in differential equations with symmetry (2010)
  13. Band, L. R.; Riley, D. S.; Matthews, P. C.; Oliver, J. M.; Waters, S. L.: Annular thin-film flows driven by azimuthal variations in interfacial tension (2009)
  14. Ma, Jingtang; Jiang, Yingjun: Moving mesh methods for blowup in reaction-diffusion equations with traveling heat source (2009)
  15. Ma, Jingtang; Jiang, Yingjun; Xiang, Kaili: Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method (2009)
  16. Ha, Youngsoo; Kim, Yong-Jung; Myers, Tim G.: On the numerical solution of a driven thin film equation (2008)
  17. Russell, R. D.; Williams, J. F.; Xu, X.: MOVCOL4: A moving mesh code for fourth-order time-dependent partial differential equations (2007)