Stochastic Homogenization of Functionals Defined on Finite Partitions

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This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

We show in full generality the stability of optimal transport paths in branched transport: namely, we prove that any limit of optimal transport paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book Optimal trans ...

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In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

In regions with low to moderate seismicity, unreinforced masonry (URM) is commonly used for the construction of low to mid-rise buildings. When these structures are subjected to seismic loading, the stiff URM walls attract considerable part of the lateral ...

Organic sensitizers comprising of donor, electron-conducting, and anchoring groups are designed and developed for dye-sensitized solar cell applications. A solar cell employing 3-(5'-{4-[bis-(4-hexyloxy-phenyl)-amino]-phenyl}-[2,2']bithiophenyl-5-yl)-2-cya ...

Stochastic Homogenization of Functionals Defined on Finite Partitions

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Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

On the Well-Posedness of Branched Transportation

An Efficient Approach to Fabricate Air-Stable Perovskite Solar Cells via Addition of a Self-Polymerizing Ionic Liquid

Minimizing the Trade-Off between Photocurrent and Photovoltage in Triple-Cation Mixed-Halide Perovskite Solar Cells

RbF post deposition treatment for narrow bandgap Cu(In, Ga)Se-2 solar cells

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Force-displacement response of unreinforced masonry walls for seismic design

Highly Efficient Organic Sensitizers for Solid-State Dye-Sensitized Solar Cells