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The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale is analyzed. Full elliptic regularity independent of is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the scale of the solution with work independent of and without analytical homogenization are introduced. Robust in error estimates for the two-scale FE spaces are proved....
The convergence of a two-scale FEM for elliptic problems in
divergence form with coefficients and geometries oscillating at
length scale ε << 1 is analyzed.
Full elliptic regularity independent of is shown
when the solution is viewed as mapping from the slow into the fast scale.
Two-scale FE spaces which are able to resolve the scale of the
solution with work independent of and without
analytical homogenization are introduced. Robust
in error estimates for the two-scale FE spaces
are...
Arbitrage-free prices of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) . This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the -scheme in time and a wavelet Galerkin method with degrees of freedom in log-price space. The dense matrix for can be replaced by a sparse matrix in the wavelet basis, and the linear...
Arbitrage-free prices of European contracts on risky assets whose
log-returns are modelled by Lévy processes satisfy
a parabolic partial integro-differential equation (PIDE)
.
This PIDE is localized to
bounded domains and the error due to this localization is
estimated. The localized PIDE is discretized by the
-scheme in time and a wavelet Galerkin method with
degrees of freedom in log-price space.
The dense matrix for can be replaced by a sparse
matrix in the wavelet basis, and the linear...
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