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Douglas–Rachford algorithm for optimal control problems
No full texthttp://dx.doi.org/10.1017/S000497271200033
A proof of Hirschhorn's conjecture on -dissection of Euler's product
No full texthttp://dx.doi.org/10.1017/S000497271200033
On nonnner automorphisms of some finite -groups: on non-inner automorphism
No full texthttp://dx.doi.org/10.1017/S000497271200033
A mixed finite element method for curve diffusion flow using a biorthogonal system
No full textFinite element methods for higher order parabolic curve flow are reasonably well established since the pioneering work of Dzuik, Kuwert and Schätzle [SIAM J. Math. Anal., 33(5):1228–1245, 2002].We develop here a new finite element scheme for a corresponding system of two second order equations for the curve diffusion flow using a biorthogonal system. This approach improves accuracy and efficiency over other methods.
References
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G. Dziuk. Convergence of a semi-discrete scheme for the curve shortening flow. Math. Mod. Meth. Appl. Sci. 4.04 (1994), pp. 589–606. doi: 10.1142/S0218202594000339
G. Dziuk. Discrete anisotropic curve shortening flow. SIAM J. Num. Anal. 36.6 (1999), pp. 1808–1830. doi: 10.1137/S0036142998337533
G. Dziuk, E. Kuwert, and R. Schätzle. Evolution of elastic curves in \Rn: Existence and computation. SIAM J. Math. Anal. 33.5 (2002), pp. 1228–1245. doi: 10.1137/S0036141001383709
M. Edwards, A. Gerhardt-Bourke, J. McCoy, G. Wheeler, and V.-M. Wheeler. The shrinking figure eight and other solitons for the curve diffusion flow. The mechanics of ribbons and Möbius bands. Ed. by R. Fosdick and E. Fried. Dordrecht: Springer Netherlands, 2016, pp. 191–211. doi: 10.1007/978-94-017-7300-3_11 C3, C11, C13).
B. P Lamichhane. A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems. J. Sci. Comput. 46 (2011), pp. 379–396. doi: 10.1007/s10915-010-9409-7
W. W. Mullins. Theory of thermal grooving. J. Appl. Phys. 28.3 (1957), pp. 333–339. doi: 10.1063/1.1722742
G. Wheeler. On the curve diffusion flow of closed plane curves. In: Ann. Mat. Pura Appl. 192.5 (2013), pp. 931–950. doi: 10.1007/s10231-012-0253-2
T. Wick. Numerical methods for partial differential equations. In: Lecture notes. Institutionelles Repositorium der Leibniz Universität Hannover, 2022. doi: 10.15488/1170
Bounds for moments of quadratic Dirichlet character sums
No full texthttp://dx.doi.org/10.1017/S000497271200033
Extremal graphs for degree sums and dominating cycles
No full texthttp://dx.doi.org/10.1017/S000497271200033
Multiplicative functions -additive on generalised octagonal numbers
No full texthttp://dx.doi.org/10.1017/S000497271200033