»ã±¨±êÌâ (Title)£ºThird order accurate, linear numerical scheme for epitaxial thin film growth model with energy stability£¨±íÑÓ±¡Ä¤³É³¤Ä£Ð͵ÄÈý½×Ïß»úÄÜÁ¿²»±äÊýÖµÌåʽ£©

»ã±¨ÈË (Speaker)£º Íõ³É ½ÌÊÚ£¨University of Massachusetts Dartmouth£©

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ21ÈÕ(ÖÜÈý) 8:30

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飨ID£º931-330-657£©

Ô¼ÇëÈË(Inviter)£º¶Î³É»ª

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A few linear schemes for nonlinear PDE model of thin film growth model without slope selection are presented in the talk. In the first order linear scheme, the idea of convex-concave decomposition of the energy functional is applied, and the particular decomposition places the nonlinear term in the concave part of the energy, in contrast to a standard decomposition. As a result, the numerical scheme is fully linear at each time step and unconditionally solvable, and an unconditional energy stability is guaranteed by the convexity splitting nature of the numerical scheme. To improve the numerical accuracy, a linear second order scheme is presented and analyzed, so that the energy stability is assured, with a second order Douglas-Dopnt regularization. Finally, a third order accurate ETD-based scheme is proposed, in which all the nonlinear terms are updated by higher order Lagrange extrapolation formulas. Moreover, the energy stability analysis and convergence estimate are established at a theoretical Level, which is the first such result in the area. Some numerical simulation results are also presented in the talk.