Multiadaptive Galerkin methods for ODEs III: A priori error estimates
Journal article, 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
Author
Anders Logg
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 43 6 2624-2646Subject Categories
Mathematics
Computational Mathematics
DOI
10.1137/040604133