Multiadaptive Galerkin methods for ODEs III: A priori error estimates

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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

Individual time steps

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