The Faculty of Mathematics and Natural Sciences: Browsing Mathematisch-Naturwissenschaftliche Fakultät by Author "Li, Guanglian"
Now showing items 1-5 of 5
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Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
Li, Guanglian; Peterseim, Daniel; Schedensack, Mira (2016-06)We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard ... -
Low-rank approximation to heterogeneous elliptic problems
Li, Guanglian (2017-03)In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov <em>n</em>-width and asymptotic expansion. This class of problems arises in practical applications ... -
On the decay rate of the singular values of bivariate functions
Griebel, Michael; Li, Guanglian (2017-11)In this work, we establish a new truncation error estimate of the singular value decomposition (SVD) for a class of Sobolev smooth bivariate functions <em>κ</em> ∈ <em>L<sup>2</sup></em>(Ω, <em>H<sup>s</sup></em>(<em>D</em>)), ... -
On the degree of ill-posedness of multi-dimensional magnetic particle imaging
Kluth, Tobias; Jin, Bangti; Li, Guanglian (2017-12)Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has ... -
On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data
Griebel, Michael; Li, Guanglian; Rieger, Christian (2021-12)Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro–differential equations with uncertainties in the ...