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

• A. Javed, K. Mitra, & I.S. Pop. Robust and adaptive linearization scheme for doubly degenerate evolution equations.

2025

• P. Braam, J.H.M ten Thije Boonkkamp, M.J.H. Anthonissen, K. Mitra, R. Beltman, & W.L. IJzerman (2025). Inverse freeform design of a parallel-to-two-target reflector system. Journal of the Optical Society of America A, Vol. 42 (8), 1133-1143.
• R. Hacking, L. Kusch, K. Mitra, M.J.H. Anthonissen, & W.L. IJzerman (2025). A neural network approach for solving the Monge-Ampère equation with transport boundary condition. Journal of Computational Mathematics and Data Science: 100119.
• R.K.H. Smeets, K. Mitra, S. Sonner, & I.S. Pop (2025). Robust time-discretisation and linearisation schemes for singular and degenerate evolution systems modelling biofilm growth. IMA Journal of Numerical Analysis (to appear).
• S. Verma, L. Kusch, K. Mitra, M.J.H. Anthonissen, J.H.M. ten Thije Boonkkamp, & W.L. IJzerman (2025). Design of a three-dimensional parallel-to-point imaging system based on inverse methods. arXiv preprint arXiv:2507.02507.
• K. Mitra, & S. Sonner (2025). Well-posedness and properties of nonlinear coupled evolution problems modelling biofilm growth. Mathematical Methods in the Applied Sciences (to appear)

2024

• J.H.M. ten Thije Boonkkamp, K. Mitra, M.J.H. Anthonissen, L. Kusch, P. Braam, & W.L. IJzerman (2025). Inverse methods for freeform optical design. Frontiers: Optics and Photonics, vol. 13.
• 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. ENUMATH Proceedings (accepted), 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.
• 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

• [2025 Apr] Invited talk at Netherlands Mathematical Congress.
• [2025 Apr] Friedrich-Schiller-Universität Jena, Jena, Germany: invited research visit.
• [2025 Mar] Invited research visit at Kanazawa University and ASHBI Kyoto University in Japan. Invited talk at MNANP2025.
• [2024 Oct] Numerics of PDEs group, TU Wien, Vienna, Austria: invited research visit.
• [2023 Dec] MOX, Politecnico de Milano, Milan, Italy: invited speaker.
• [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

2025	MNANP2025 (Japan), ENUMATH (Germany), INTRUSION (Italy)
2024	CMAM (Germany), Algoritmy (Slovakia)
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)

Review work

PhD Defense Committees

2024

Mostafa Meliani

Radboud University

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