Institute for
Numerical Simulation

Research Group
A. Chernov

Research Interests

My research concentrates on construction, analysis and efficient implementation of numerical methods for partial differential and integral equations (PDEs and IEs). In particular

• Numerical solution of linear and nonlinear problems with random input data, problems in stochastic domains or in a stochastic medium
• Fast methods for high-dimensional problems, Sparse Grids, Sparse Spectral FEM
• Discretization of nonlocal operators
• Efficient numerical integration of singularities
• Nonlinear PDEs and IEs, variational inequalities, a posteriori error control
• p- and hp-versions of FEM, BEM and FE-BE coupling
• non-conforming discretization methods for interface problems

Projects

• Research project "Numerical Methods for Stochastic and Parametric Obstacle Problems",
  funded by the Hausdorff Center for Mathematics, period: August 2012 – July 2014,
  Assistant: MSc Claudio Bierig (Univ. Bonn)


• Research project "Numerical methods for stochastic transmission problems", (ID 56266715)
  DAAD, funded by the Federal Ministry of Education and Research (BMBF), period January – December 2013,
  Project partner: A/Prof. Thanh Tran (UNSW Sydney)
  Assistants: Dr. Duong Pham (Univ. Bonn), Kim-Ngan Le (UNSW Sydney)


• Hausdorff Center for Mathematics, Research Area J: High-dimensional problems and multi-scale methods


• Hausdorff Center for Mathematics, Research Area G: Stochastics in discrete, singular and infinite dimensional structures