Christoph Erath, Mark A. Taylor and Ramachandran D. Nair
. Taylor, S. J. Thomas, and H. M. Tufo, High resolution mesh convergence properties and parallel efficiency of a spectral element atmospheric dynamical core, International Journal of High Performance Computing Applications, vol. 19, pp. 225-235, 2005.
7. R. Sadourny, Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids, Monthly Weather Review, vol. 100, pp. 136-144, 1972.
8. O. Guba, M. A. Taylor, and A. St-Cyr, Optimization-based limiters for the spectralelementmethod, Journal of
M. Rucka, W. Witkowski, J. Chróscielewski and K. Wilde
with transverse crack, Finite Elements in Analysis and Design 40, 1729-1751, 2004.
4. T. Patera, A spectralelementmethod for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics 54, 468-488, 1984.
5. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer Verlag, Berlin, Heidelberg 1998.
6. R. Sridhar, A. Chakraborty, S. Gopalakrishnan, Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using
Nejmeddine Chorfi, Mohamed Abdelwahed and Ines Ben Omrane
In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler’s implicit scheme in time and spectral method in space. We propose two families of error indicators both of them are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.
Research 104, 81–90, 2015
5. M. Piekarczyk, R. Grec, Application of adhesive bonding in steel and aluminium structures, Archives of Civil Engineering, 58, 309–329, 2012
6. M. Rucka, Wave Propagation in Structures. Modelling, Experimental Studies and Application to Damage Detection, Wydawnictwo Politechniki Gdańskiej, Gdańsk 2011
7. M. Rucka, Modelling of in-plane wave propagation in a plate using spectralelementmethod and Kane-Mindlin theory with application to damage detection. Archive of Applied Mechanics 81, 1877–1888, 2011
8. M. Rucka, W
, vol. 44, no. 26, p. 265301, 2011.
4. S. Shao, T. Lu, and W. Cai, Adaptive conservative cell average spectralelementmethods for transient Wigner equation in quantum transport, Communications in Computational Physics, vol. 9, no. 3, pp. 711-739, 2011.
5. A. Dorda and F. Schürrer, A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes, Journal of Computational Electronics, vol. 284, pp. 95-116, 2015.
6. Y. Xiong, Z. Chen, and S
1. O. Morandi and L. Demeio, A Wigner-function approach to interband transitions based on the multiband-envelope-function model, Transp. Theor. Stat. Phys., vol. 37, no. 5-7, pp. 473-459, 2008.
2. O. Morandi and F. Schürrer, Wigner model for quantum transport in graphene, J. Phys. A: Math. Theor., vol. 26, p. 265301, 2011.
3. S. Shao, T. Lu, and W. Cai, Adaptive conservative cell average spectralelementmethods for transient Wigner equation in quantum transport, Comm. Comput. Phys., vol. 9, no. 3, pp
. ADVANCES IN SCIENCE AND TECHNOLOGY-RESEARCH JOURNAL, 12, 157-163.
PN-EN 1369:2013-04. Founding. Magnetic particle testing. PKN, Warszawa
PN-EN ISO 9934-1:2017-02. Non-destructive testing. Magnetic particle testing. Part 1: General principles, PKN, Warszawa
Rosenkrantz, E., Bottero, A., Komatitsch, D. et al. 2019. A flexible numerical approach for non-destructive ultrasonic testing based on a time-domain spectral-elementmethod: Ultrasonic modeling of Lamb waves in immersed defective structures and of bulk waves in damaged anisotropic materials , NDT
17. K. W. Morton, On the analysis of finite volume methods for evolutionary problems., SIAM Journal of Numerical Analysis, vol. 35, pp. 2195-2222, 1998.
18. F. Giraldo, The Lagrange-Galerkin spectralelementmethod on unstructured quadrilateral grids., Journal of Computational Physics, vol. 147, pp. 114-146, 1998.
19. D. Xiu and G. E. Karniadakis, A semi-Lagrangian High-Order Method for Navier-Stokes Equations., Journal of Computational Physics, vol. 172, pp. 658-684, 2001.
20. C. Zhao, B. Hobbes, H. Mühlhaus, and A
mantle beneath Eurasia. Geophys. J. Int., 174 , 978–992.
Kustowski B., Ekstrom G., Dziewonski A. M., 2008b: Anisotropic shear-wave velocity structure of the Earth’s mantle: A global model. J. Geophys. Res., 113 , B06306.
Lekic V., Romanowicz B., 2011: Inferring upper-mantle structure by full waveform tomography with the spectralelementmethod. Geophys. J. Int., 185 , 2, 799–831.
Laske G., Masters G., Ma Z., Pasyanos M. E., 2012: CRUST1.0: An updated global model of Earth’s crust. Geophys. Res. Abs., 14 , EGU2012-3743-1, EGU General Assembly 2012