For us there is no ignorabimus, and in my opinion none whatever in natural science. 
In opposition to the foolish ignorabimus our slogan shall be:

'We must know — we will know'

~ David Hilbert

I am fascinated by how partial differential equations can explain the world around us.


  • Applied analysis: Nonlinear degenerate PDEs, well-posedness, Rothe's method, free boundaries.
  • Numerical analysis: Linear iterative techniques, a-posteriori error estimates, domain decomposition schemes, spatial discretizations including finite differences, elements, volumes.
  • Scientific computing: Adaptivity, data-driven simulations, post-processing and visualization, parallelization, ODE solvers, meshing, linear solvers.
  • Modelling:
    • Multiphase flow in porous medium, particularly, hysteresis and dynamic effects.
    • Mathematical biology, in particular, biofilm growth.
  • Special solutions: Travelling waves, similarity solutions, entropy solutions, Riemann problems.
  • Asymptotic analysis and upscaling: Homogenization, stability analysis, phase-fields.

A general summary of my work on hysteresis and dynamic effects

My Publications

In preparation

  • K. Mitra, & M. Vohralik. Robust, reliable, & efficient a posteriori estimates for nonlinear elliptic problems: An orthogonal decomposition result based on iterative linearization.


Invited Talks & Research Visits

Selected Conference Talks

2022 INTERPORE (UAE), Computational Methods in Water Resources (CMWR) (Poland)
2020-21 European Finite Element Fair (France), INTERPORE (online), INRIA-IFPN meet (France)
2019 ICIAM (Spain), SIAM Geosciences (USA), INTERPORE (Spain)
2017-18 INTERPORE (USA), ACOMEN (Belgium), ENUMATH (Norway), MAMERN VII (Morocco), JMBC Burgers Symposium (The Netherlands)

Peer Reviews in Journals & Proceedings

  • SIAM Journal on Scientific Computing
  • Applied Mathematics & Computation
  • Advances in Water Resources
  • Computational Geosciences
  • Journal of Comp. & App. Mathematics
  • Journal of Num. Anal. & Appr. Theory
  • Society of Petroleum Engineering Journal
  • Transport in Porous Media
  • Applied Numerical Mathematics
  • ENUMATH 2017 Proceedings