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 Hilbert

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

|| Expertise || Publications || Outreach|| Reviews

Expertise

• Applied analysis: Nonlinear degenerate PDEs, well-posedness, Rothe's method, free boundaries.
• Numerical analysis: Iterative methods, 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.
• Illumination optics.
• 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

• R.K.H. Smeets, K. Mitra, S. Sonner, & I.S. Pop. Robust time-discretization and linearization schemes for degenerate and coupled evolution systems.
• A. Javed, K. Mitra, & I.S. Pop. Robust and adaptive linearization scheme for doubly degenerate evolution equations.

2024

• K. Mitra, A. Ratz, & B. Schweizer (2024). Travelling wave solutions for gravity fingering in porous media flows. Journal of Differential Equations, 394, 120-151.
• K. Mitra, & M. Vohralik (2024). A posteriori error estimates for the Richards equation. Mathematics of Computation, 93, 1053-1096.
• K. Mitra, Q. Peng, & C. Reisch (2024). Studying wildfire fronts using advection-diffusion-reaction models. arXiv:2401.17468v1.



2023

• K. Mitra, & M. Vohralik (2023). Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based on iterative linearization. HAL Preprint, hal-04156711, v.1.
• 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 . Computers & Mathematics with Applications, 152, 155-167.



2022

• K. Mitra, J.M. Hughes, S. Sonner, H.J. Eberl, & J.D. Dockery (2022). Travelling Waves in a PDE–ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion. Journal of Dynamics and Differential Equations, 1-35.



2021

• 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.



2020

• 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.



2019

• 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.



2018

• 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.

Outreach

Invited Talks & Research Visits

• [2023 Nov] Workshop on Interdisciplinary Research in Ecological & Mathematical Analysis of Wildfire Hazards, Braunschweig, Germany.
• [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
• [2022 Mar] Porous Media Tea Time Talks , InterPore Society: Invited for a YouTube live talk.
  
• [2022, 2019] INRIA Paris, France: invited to the SERENA group for collaboration and seminar talks.
  
• [2022, 2018] MF Oberwolfach, Germany: invited to attend the workshop.
  
• [2019 Jan] Student Trip organized by University of Bergen, Norway: gave invited talks in KTH Stockholm, & Chalmers University of Technology in Gothenburg.
  
• [2018, 2019] University of Stuttgart, Germany: invited for a talk and collaboration.
  
• [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

2023	SIAM Geosciences (Norway), ENUMATH (Portugal)
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 Water Resources Research 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 International Journal of Num. Anal. & Modeling ENUMATH 2017 Proceedings