Browsing by Author "Kornhuber, Ralf"

Now showing 1 - 4 of 4
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    Fractal homogenization of a multiscale interface problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Heida, Martin; Kornhuber, Ralf; Podlesny, Joscha
    Inspired from geological problems, we introduce a new geometrical setting for homogenization of a well known and well studied problem of an elliptic second order differential operator with jump condition on a multiscale network of interfaces. The geometrical setting is fractal and hence neither periodic nor stochastic methods can be applied to the study of such kind of multiscale interface problem. Instead, we use the fractal nature of the geometric structure to introduce smoothed problems and apply methods from a posteriori theory to derive an estimate for the order of convergence. Computational experiments utilizing an iterative homogenization approach illustrate that the theoretically derived order of convergenceof the approximate problems is close to optimal.
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    Geometric Partial Differential Equations: Surface and Bulk Processes
    (Zürich : EMS Publ. House, 2015) Elliott, Charles M.; Kornhuber, Ralf; Sethian, James A.
    The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems.
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    Geometric Partial Differential Equations: Theory, Numerics and Applications
    (Zürich : EMS Publ. House, 2011) Elliott, Charles M.; Huisken, Gerhard; Kornhuber, Ralf
    This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications.
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    Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures
    (Zürich : EMS Publ. House, 2019) Garcke, Harald; Kornhuber, Ralf
    Partial differential equations in complex domains with free\linebreak boundaries and interfaces continue to be flourishing research areas at the interfaces between PDE theory, differential geometry, numerical analysis and applications. Main themes of the workshop have been PDEs on evolving domains, phase field approaches, interactions of bulk and surface PDEs, curvature driven evolution equations. Applications particular from biology, such as cell and cancer modelling and fluid as well solid mechanics have been subjects of the conference.