Acta Numerica 2009:
Cambridge University Press, May 28, 2009 - Mathematics - 352 pages
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques and analysis.
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Adaptivity with moving grids
Fast direct solvers for integral equations in complex
Blowup or no blowup? A uniﬁed computational
3D Euler equations 3D model 3D Navier-Stokes equations adaptive mesh adaptive method algorithm analysis approximation blow-up boundary breaking points Budd calculation collocation method computational domain conservation law consider continuous RK method convergence deﬁned Deﬁnition delay differential equations derivatives dimensions discontinuity dynamic equidistribution Euler equations example ﬁeld Figure ﬁnd ﬁnite-time singularity ﬁrst ﬁxed Fourier smoothing method given global order global regularity grid hn+1 Huang and Russell initial data integration interpolation interval linear Lipschitz-continuous Math matrix maximum vorticity mesh points MMPDE monitor function moving mesh methods Navier-Stokes equations non-blow-up nonlinear obtained ODES order q partial differential equations Phys polynomial problems pseudo-spectral method r-adaptive resolution RFDEs right-hand side Rokhlin satisﬁes scaling Section self-similar self-similar solutions SIAM signiﬁcant singular solutions solver solving spectral methods step-size symmetry Tang Theorem tion triangles underlying PDE uniform mesh uniform order velocity vortex stretching vortex tubes vorticity