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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 6
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Articles

L(L2) and L(H1) norms error estimates in finite element methods for electric interface model

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Pages 1351-1370 | Received 30 Jun 2018, Accepted 09 Jul 2019, Published online: 18 Jul 2019

References

  • Ammari H, Chen DH, Zou J. Well-Posedness of an electric interface model and its finite element approximation. Math Models Methods Appl Sci. 2016;26:601–625. doi: 10.1142/S0218202516500111
  • Rems L, Ušaj M, Kandušer M, et al. Cell electrofusion using nanosecond electric pulses. Sci Rep. 2013;3:3382. doi: 10.1038/srep03382
  • Wang X, Zou J. Identification of conductivity and permittivity in a pulsed electric field model. Appl Anal. 2016;95:2736–2749. doi: 10.1080/00036811.2015.1107547
  • Angersbach A, Heinz V, Knorr D. Effects of pulsed electric fields on cell membranes in real food systems. Innov Food Sci Emerg Technol. 2000;1:135–149. doi: 10.1016/S1466-8564(00)00010-2
  • Markxa GH, Daveyb CL. The dielectric properties of biological cells at radio frequencies: applications in biotechnology. Enzyme Microb Technol. 1999;25:161–171. doi: 10.1016/S0141-0229(99)00008-3
  • Miklavcic D, Pavselj N, Hart FX. Electric properties of tissues. New York: Wiley Encyclopedia of Biomedical Engineering; 2006.
  • Polevaya Y, Ermolina I, Schlesinger M, et al. Time domain dielectric spectroscopy study of human cells II. Normal and malignant white blood cells. Biochim Biophys Acta. 1999;1419:257–271. doi: 10.1016/S0005-2736(99)00072-3
  • Schwan HP. Mechanism responsible for electrical properties of tissues and cell suspensions. Med Prog Technol. 1993;19:163–165.
  • Hu Q, Joshi RP. Transmembrane voltage analyses in spheroidal cells in response to an intense ultrashort electrical pulse. Phys Rev E. 2009;79:011901.
  • Kotnik T, Miklavcic D, Slivnik T. Time course of transmembrane voltage induced by time-varying electric fields-a method for theoretical analysis and its application. Bioelectrochem Bioenerg. 1998;45:3–16. doi: 10.1016/S0302-4598(97)00093-7
  • Weaver JC, Chizmadzhev Y. Theory of electroporation: a review. Bioelectrochem Bioenerg. 1996;41:135–160. doi: 10.1016/S0302-4598(96)05062-3
  • Andr F, Mir LM. DNA electrotransfer: Its principles and an updated review of its therapeutic applications. Gene Ther. 2004;11:S33–S42. doi: 10.1038/sj.gt.3302367
  • Elham Salimi. Nanosecond pulse electroporation of biological cells: the effect of membrane dielectric relaxation [thesis]. Ireland: Department of Electrical and Computer Engineering, University of Manitoba; 2011.
  • Butson CR, McIntryre CC. Tissue and electrode capacitance reduce neural activation volumes during deep brain stimulation. Clin Neuriphys. 2005;116:2490–2500. doi: 10.1016/j.clinph.2005.06.023
  • Grill WM. Modeling the effects of electric fields on nerve fibers: influence of tissue electrical properties. IEEE Trans Biomed Eng. 1999;46:918–928. doi: 10.1109/10.775401
  • Yang L. Electrical impedance spectroscopy for detection of bacterial cells in suspensions using interdigitated microelectrodes. Talanta. 2008;74:1621–1629. doi: 10.1016/j.talanta.2007.10.018
  • Schoenbach KH, Peterkin FE, Alden RW, et al. The effect of pulsed electric fields on biological cells: experiments and applications. IEEE Trans Plasma Sci. 1997;25:284–292. doi: 10.1109/27.602501
  • Ammari H, Garnier J, Giovangigli L, et al. Spectroscopic imaging of a dilute cell suspension. J Math Pure Appl. 2016;105:603–661. doi: 10.1016/j.matpur.2015.11.009
  • Adams RA, Fournier JJF. Sobolev spaces. 2nd ed. Amsterdam: Academic Press; 2003.
  • Li JZ, Melenk JM, Wohlmuth B, et al. Optimal a priori estimates for higher order finite elements for elliptic interface problems. Appl Numer Math. 2010;60:19–37. doi: 10.1016/j.apnum.2009.08.005
  • Deka B. Finite element methods with numerical quadrature for elliptic problems with smooth interfaces. J Comput Appl Math. 2010;234:605–612. doi: 10.1016/j.cam.2009.12.052
  • Robinson JC. Infinite-Dimensional dynamical system: an introduction to dissipative parabolic PDEs and the theory of global attractors. Cambridge: Cambridge Texts in Applied Mathematics; 2001.
  • Thomée V. Galerkin finite element methods for parabolic problems. New York: Springer-Verlag; 1997.
  • Deka B, Sinha RK. L∞(L2) and L∞(H1) norms error estimates in finite element method for linear parabolic interface problems. Numer Funct Anal Optim. 2011;32:267–285. doi: 10.1080/01630563.2010.532272
  • Köppl T, Vidotto E, Wohlmuth B, et al. Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions. Math Models Methods Appl Sci. 2018;28:953–978. doi: 10.1142/S0218202518500252
  • Nikolić V, Kaltenbacher B. On higher regularity for the Westervelt equation with strong nonlinear damping. Appl Anal. 2016;95:2824–2840. doi: 10.1080/00036811.2015.1114607

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