Error estimates for the numerical solution of a time-periodic linear parabolic problem

• In this paper we consider the numerical solution of a time-periodic linear parabolic problem. We derive optimal order error estimates in Lz(f2) for approximate solutions obtained by discretizing in space by a Galerkin finite-element method and in time by single-step finite difference methods, using known estimates for the associated initial value problem. We generalize this approach and obtain error estimates for more general discretization methods in the norm of a Banach space B c L2(Ω), e.g., B = H10(Ω) or L∞(Ω). Finally, we consider some computational aspects and give a numerical example.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

AMS 1980 subject classification: 65N15

65N30

error estimate

Galerkin method

parabolic

time-periodic

MATHEMATICS

MATEMATIK

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