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We propose and analyse a new finite-element method for convection–diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin (DG) method for the hyper-bolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate(More)
This paper investigates the stable identification of local volatility surfaces σ(S, t) in the Black-Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of the parameter-to-solution mapping, which assigns option prices to given volatilities, we show stability and convergence of approximations gained by Tikhonov(More)
In this paper we investigate convergence of Landweber iteration in Hilbert scales for linear and nonlinear inverse problems. As opposed to the usual application of Hilbert scales in the framework of regularization methods, we focus here on the case s ≤ 0, which (for Tikhonov regularization) corresponds to regularization in a weaker norm. In this case, the(More)
This manuscript deals with the hp error analysis of a hybrid discontinuous Galerkin method for incompressible flow. Besides the usual coercivity and boundedness estimates, we establish the inf-sup stability for the discrete incompressibility constraint with a constant, which is only slightly sub-optimal with respect to the polynomial degree. This result(More)
Correct pricing of options and other financial derivatives is of great importance to financial markets and one of the key subjects of mathematical finance. Usually, parameters specifying the underlying stochastic model are not directly observable, but have to be determined indirectly from observable quantities. The identification of local volatility(More)
The conjugate gradient method applied to the normal equations (cgne) is known as one of the most efficient methods for the solution of (non-symmetric) linear equations. By stopping the iteration according to a discrepancy principle, cgne can be turned into a regularization method. We show that cgne can be accelerated by preconditioning in Hilbert scales,(More)
There is ongoing controversy about the mechanisms that determine the characteristics of the glomerular filter. Here, we tested whether flow across the glomerular filter generates extracellular electrical potential differences, which could be an important determinant of glomerular filtration. In micropuncture experiments in Necturus maculosus, we measured a(More)
In this paper we consider the regularization of the inverse problem of diffuse optical tomography by standard regularization methods with quadratic penalty terms. We therefore investigate in detail the properties of the associated forward operators, and derive continuity and differentiability results, which are based on derivation of W 1,p regularity(More)
We propose and analyse a new finite element method for convection diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin method for the hyperbolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate(More)