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Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: adjoint approximations and extensions

Abstract:

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It...

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M.B. Giles More by this author
S. Ulbrich More by this author
Publication date:
2010
URN:
uuid:322eb67d-e78d-4a73-bbc5-d5fa9a6af999
Local pid:
oai:eprints.maths.ox.ac.uk:1686

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