Wavelet Discretizations of Parabolic Integrodifferential Equations
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Date
2003-02
Publication Type
Journal Article
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yes
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Abstract
We consider parabolic problems u+Au=f in (0,T)×Ω, T<∞, where Ω⊂R is a bounded domain and A is a strongly elliptic classical pseudodifferential operator of order ρ∈[0,2] in H~ρ/2(Ω). We use a θ-scheme for time discretization and a Galerkin method with N degrees of freedom for space discretization. The full Galerkin matrix for A can be replaced with a sparse matrix using a wavelet basis, and the linear systems for each time step are solved approximatively with GMRES. We prove that the total cost of the algorithm for M time steps is bounded by O(M N(logN)β) operations and O(N(logN)β) memory. We show that the algorithm gives optimal convergence rates (up to logarithmic terms) for the computed solution with respect to L2 in time and the energy norm in space.
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published
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Journal / series
Volume
41 (1)
Pages / Article No.
159 - 180
Publisher
SIAM
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Subject
Parabolic integrodifferential equation; Levy-process; Wavelet compression; Discontinuous; Galerkin method
Organisational unit
03435 - Schwab, Christoph / Schwab, Christoph