Multiadaptive Galerkin methods for ODEs III: A priori error estimates
Artikel i vetenskaplig tidskrift, 2006

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.

Individual time steps

Discontinuous Galerkin

mdG(q)

ODE

mcG(q)

Interpolation estimates

Existence

Multiadaptivity

A priori error estimates

Continuous Galerkin

Stability

Peano kernel theorem

Piecewise smooth

Local time steps

Författare

Anders Logg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 43 2624-2646

Ämneskategorier

Matematik

Beräkningsmatematik

DOI

10.1137/040604133