Research
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 HilbertI am fascinated by how partial differential equations can explain the world around us.
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Expertise
- 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.
- K. Mitra, & S. Sonner (2023). Well-posedness and properties of nonlinear coupled evolution problems modelling biofilm growth. arXiv:2304.00175.
- A. Harnist, K. Mitra, A. Rappaport, & M. Vohralik (2023). Robust a posteriori estimate of energy differences for nonlinear elliptic problems. HAL preprint, hal-04033438.
- J.S. Stokke, K. Mitra, E. Storvik, J.W. Both, & F.A. Radu (2023). An adaptive solution strategy for Richards' equation. arXiv:2301.02055.
- K. Mitra, J.M. Hughes, S. Sonner, H.J. Eberl, & J.D. Dockery (2022). Travelling waves in a PDE--ODE coupled system with nonlinear diffusion. Journal of Dynamics and Differential Equations (to appear).
- K. Mitra, & M. Vohralik (2021). A posteriori error estimates for the Richards equation. HAL Preprint, hal-03328944.
- K. Mitra, & C.J. van Duijn (2021). Capillary hysteresis and gravity segregation in two phase flow through porous media. Computational Geosciences, 26(1), 101-114.
- K. Mitra. (2021). Existence and properties of solutions of the extended play-type hysteresis model. Journal of Differential Equations, 288, 118-140.
- K. Mitra, A. Ratz, & B. Schweizer (2020). Travelling wave solutions for gravity fingering in porous media flows. arXiv:2011.10792.
- K. Mitra, T. Koeppl, I.S. Pop, C.J. van Duijn, & R. Helmig (2020). Fronts in two-phase porous media flow problems: the effects of hysteresis and dynamic capillarity. Studies in Applied Mathematics, 144(4), 449-492.
- E.E. Behi-Gornostaeva, K. Mitra, & B. Schweizer (2019). Traveling wave solutions for the Richards equation with hysteresis. IMA Journal of Applied Mathematics, 84(4), 797-812.
- K. Mitra, & C.J. van Duijn (2019). Wetting fronts in unsaturated porous media: the combined case of hysteresis and dynamic capillary pressure. Nonlinear Analysis: Real World Applications, 50, 316-341.
- X. Cao, & K. Mitra (2019). Error estimates for mixed finite element for two-phase porous media flow with dynamic capillarity. Journal of Computational and Applied Mathematics, 353, 164-178.
- K. Mitra, & I.S. Pop (2019). A modified L-Scheme to solve nonlinear diffusion problems. Computers and Mathematics with Applications, 77, 1722-1738.
- C.J. van Duijn, & K. Mitra (2018). Hysteresis and horizontal redistribution in porous Media. Transport in Porous Media, 122, 375-399.
- D. Seus, K. Mitra, I.S. Pop, F.A. Radu, & C. Rohde (2018). A linear domain decomposition method for partially saturated flow in porous media. Computer Methods in Applied Mechanics and Engineering, 333, 331-355.
- C.J. van Duijn, K. Mitra, & I.S. Pop (2018). Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure. Nonlinear Analysis: Real World Applications, 41, 232-268.
2023
2022
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2019
2018
Outreach
Invited Talks & Research Visits
- [2023 Jul] Lorentz center workshop on Analysis & numerics of nonlinear PDEs: degeneracies & free boundaries, Leiden, The Netherlands.
- [2022 Sep] CSD Seminar, Porous Media Group, Bergen, Norway.
- [2022 Jun] Summer school: CEA-EDF-Inria summer school: Certification of errors in numerical simulations, Paris, France: invited to give lectures on methods for nonlinear equations
- [2022 Jun] Workshop on Interplay of discretization and algebraic solvers: a posteriori error estimates and adaptivity, Paris, France: invited speaker
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[2022 Mar] Porous Media Tea Time Talks , InterPore Society: Invited for a YouTube live talk.
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[2022, 2019] INRIA Paris, France: invited to the SERENA group for collaboration and seminar talks.
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[2022, 2018] MF Oberwolfach, Germany: invited to attend the workshop.
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[2019 Jan] Student Trip organized by University of Bergen, Norway: gave invited talks in KTH Stockholm, & Chalmers University of Technology in Gothenburg.
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[2018, 2019] University of Stuttgart, Germany: invited for a talk and collaboration.
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[2018 June] TU Dortmund, Germany: invited for a talk and collaboration.
- [2018 May] Workshop on Adaptive model and solver computations, Ullensvang, Norway: invited speaker.
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
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