Australian Mathematical Society (AustMS): E-Journals
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Ohno-Zagier type relations for multiple -values
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the Waring-Goldbach problem for one square, four cubes and one biquadrate
No full texthttp://dx.doi.org/10.1017/S000497271200033
Groups in which all large subgroups have bounded near defect
No full texthttp://dx.doi.org/10.1017/S000497271200033
Fast methods for fitting log-Gaussian Cox process models in ecology
No full texthttp://dx.doi.org/10.1017/S000497271200033
Models of flow and diffusion: Selective withdrawal from a stratified fluid and dispersal of hydrogen in the retina
No full texthttp://dx.doi.org/10.1017/S000497271200033
A pair of equations in eight prime cubes and powers of 2
No full texthttp://dx.doi.org/10.1017/S000497272200128
A novel SNP heritability model for heritability analyses and genomic prediction
No full texthttp://dx.doi.org/10.1017/S000497272300056
A mixed finite element method using a biorthogonal system for optimal control problems governed by a biharmonic equation
Get PDFIn this article, we consider an optimal control problem governed by a biharmonic equation with clamped boundary conditions. We use the Ciarlet--Raviart formulation combined with a biorthogonal system to obtain an efficient numerical scheme. We discuss the a priori error analysis and present results of the numerical experiments that validate the theoretical estimates.
References
L. Boudjaj, A. Naji, and F. Ghafrani. Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method. Eng. Anal. Bound. Elements 107 (2019), pp. 208–217. doi: 10.1016/j.enganabound.2019.07.007
W. Cao and D. Yang. Ciarlet–Raviart mixed finite element approximation for an optimal control problem governed by the first biharmonic equation. J. Comput. App. Math. 233.2 (2009), pp. 372–388. doi: 10.1016/j.cam.2009.07.039
P. G. Ciarlet. The finite element method for elliptic problems. Vol. 40. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002. doi: 10.1137/1.9780898719208.
V. Girault and P.-A. Raviart. Finite element methods for Navier–Stokes equations. Vol. 5. Springer Series in Computational Mathematics. Springer-Verlag, 1986. doi: 10.1007/978-3-642-61623-5
T. Gudi, N. Nataraj, and K. Porwal. An interior penalty method for distributed optimal control problems governed by the biharmonic operator. Comput. Math. App. 68.12 (2014), pp. 2205–2221. doi: 10.1016/j.camwa.2014.08.012
B. P. Lamichhane. A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems. J. Sci. Comput. 46.3 (2011), pp. 379–396. doi: 10.1007/s10915-010-9409-7.
B. P. Lamichhane and E. Stephan. A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems. Numer. Meth. Part. Diff. Eq. 28 (2012), pp. 1336–1353. doi: 10.1002/num.20683
J. L. Lions. Optimal control of systems governed by partial differential equations. Vol. 170. Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York-Berlin, 1971. url: https://link.springer.com/book/9783642650260
F. Tröltzsch. Optimal control of partial differential equations: Theory, methods and applications. Vol. 112. Graduate Studies in Mathematics. American Mathematical Society, 2010. doi: 10.1090/gsm/112.
G. N. Wells, E. Kuhl, and K. Garikipati. A discontinuous Galerkin method for the Cahn–Hilliard equation. J. Comput. Phys. 218 (2006), pp. 860 –877. doi: 10.1016/j.jcp.2006.03.01
Volatility swaps valuation under a modified risk-neutralized Heston model with a stochastic long-run variance level
No full textWe consider the pricing of discretely sampled volatility swaps under a modified Heston model, whose risk-neutralized volatility process contains a stochastic long-run variance level. We derive an analytical forward characteristic function under this model, which has never been presented in the literature before. Based on this, we further obtain an analytical pricing formula for volatility swaps which can guarantee the computational accuracy and efficiency. We also demonstrate the significant impact of the introduced stochastic long-run variance level on volatility swap prices with synthetic as well as calibrated parameters.
doi: 10.1017/S144618112200013