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Multiadaptive Galerkin methods for ODEs III: A priori error estimates

Anders Logg (Institutionen för matematiska vetenskaper, matematik)
SIAM Journal on Numerical Analysis (0036-1429). Vol. 43 (2006), 6, p. 2624-2646.
[Artikel, refereegranskad vetenskaplig]

The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution. © 2006 Society for Industrial and Applied Mathematics.

Nyckelord: A priori error estimates , Continuous Galerkin , Discontinuous Galerkin , Existence , Individual time steps , Interpolation estimates , Local time steps , mcG(q) , mdG(q) , Multiadaptivity , ODE , Peano kernel theorem , Piecewise smooth , Stability

Denna post skapades 2014-01-05. Senast ändrad 2014-09-29.
CPL Pubid: 191159


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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