Abhinav Jha
Assistant Professor · Department of Mathematics · IIT Gandhinagar
I work in numerical analysis and scientific computing. My PhD at Freie Universität Berlin, as a member of the Berlin Mathematical School, focused on stabilization techniques for convection-dominated problems.
As a postdoc at RWTH Aachen and the University of Stuttgart, I moved into computational chemistry, developing domain decomposition methods for Poisson–Boltzmann equations. Brief overviews: AFC schemes, ddLPB, ddPB.
Finite Element Methods
Algebraic Stabilizations
A Posteriori Error Estimation
Domain Decomposition
Implicit Solvation Models
Physics-Informed Learning
Research
Publications
Most papers are also on arXiv. If you need the published version of any of them, just write to me.
- 2026Adaptive Finite Elements with Algebraic Stabilization for Convection-Dominated TransportJournal of Computational Physics · DOI
- 2026Trace Estimates for Harmonic Functions Along Circular Arcs with Applications to Domain Decomposition on Overlapping DisksSIAM Journal on Mathematical Analysis 58, 1571–1612 · DOI
- 2026Symmetric Stabilized FEM for Time-Fractional Convection-Diffusion-Reaction EquationsMathematics and Computers in Simulation 245, 685–697 · DOI
- 2024Well-Balanced Convex Limiting for Finite Element Discretizations of Steady Convection-Diffusion-Reaction EquationsJournal of Computational Physics 518, 113305 · DOI
- 2024ddX: Polarizable Continuum Solvation from Small Molecules to ProteinsWIREs Computational Molecular Science 14, e1726 · DOI
- 2024Residual-Based a Posteriori Error Estimators for Algebraic StabilizationsApplied Mathematics Letters 157, 109192 · DOI
- 2023Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction EquationsSIAM Journal on Scientific Computing 45, B564–B589 · DOI
- 2023Linear Scaling Computation of Forces for the Domain-Decomposition Linear Poisson–Boltzmann MethodThe Journal of Chemical Physics, 104105 · DOI
- 2023An Assessment of Solvers for Algebraically Stabilized Discretizations of Convection-Diffusion-Reaction EquationsJournal of Numerical Mathematics 31, 79–103 · DOI
- 2021Hanging Nodes for Higher-Order Lagrange Finite ElementsExamples and Counterexamples 1, 100025 · DOI
- 2021A Residual Based a Posteriori Error Estimator for AFC Schemes for Convection-Diffusion EquationsComputers and Mathematics with Applications 97, 86–99 · DOI
- 2020On Basic Iteration Schemes for Nonlinear AFC DiscretizationsBAIL 2018 — Boundary and Interior Layers, LNCSE 135, 113–128 · DOI
- 2019A Study of Solvers for Nonlinear AFC Discretizations of Convection–Diffusion EquationsComputers and Mathematics with Applications 78, 3117–3138 · DOI
Preprints
- 2026Bilinearity Preserving Algebraic Flux CorrectionarXiv 2609.16830
- 2026Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential EquationsarXiv 2607.25608
- 2026Lyapunov Stability and Optimal Error Estimates for an SIPG Method for Weakly Damped Semilinear Wave EquationsarXiv 2606.13185
- 2026On the Convergence of an Adaptive Denoiser Driven Iterative Regularization with Early StoppingarXiv 2604.20360
- 2026Non-uniform α-Robust Alikhanov Mixed FEM with Optimal Convergence for the Time-Fractional Allen–Cahn EquationarXiv 2603.11696
- 2023Domain Decomposition Method for Poisson–Boltzmann Equations Based on Solvent Excluded SurfacearXiv 2309.06862
Teaching
Courses
Lecture notes, slides and assignments are freely available below.
Current · Semester 1, 2026–27
MA103
Calculus of Single Variable and Linear Algebra
Past Semesters
Summer Semester, 2026
MA103
Calculus of Single Variable
Semester 2, 2025–26
Semester 1, 2025–26
Semester 2, 2024–25
Online Workshops (NPTEL+)
Hands-on workshops on numerical methods in Python, open to students and professionals across India.
265
Participants · Feb 2026
NumPython
A Workshop on Numerical Analysis
74
Participants · May 2026
NumPython 2
A Workshop on Numerical Analysis of ODEs
138
Participants · Jun 2026
NumLinPy
Numerical Linear Algebra in Python
Background
Curriculum Vitae
A short version. The full CV is here (PDF).
Positions
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Oct 2024 – PresentAssistant Professor, Grade 1Department of Mathematics, IIT Gandhinagar
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Sep 2022 – Aug 2024Postdoctoral ResearcherUniversität Stuttgart · with Prof. Benjamin StammNumerical Mathematics for High Performance Computing
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Jan 2021 – Aug 2022Postdoctoral ResearcherRWTH Aachen University · with Prof. Benjamin StammApplied and Computational Mathematics
Education
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Oct 2017 – Oct 2020Dr. rer. nat., magna cum laudeFreie Universität Berlin · advisor Prof. Volker JohnNumerical Algorithms for Algebraic Stabilizations of Scalar Convection-Dominated Problems
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2015 – 2017M.Sc. MathematicsIIT Roorkee · advisor Prof. Ankik Kumar GiriFinite Element Method for Population Balance Equations
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2012 – 2015B.Sc. (Hons.) MathematicsSt. Stephen's College, University of Delhi
Research Grants
- Prime Minister Early Career Research Grant — ANRF, 2026-2029
Advances in Domain Decomposition Methods for Implicit Solvation Models - DST INSPIRE Faculty Award — Department of Science and Technology, 2025–2030
Algebraic Stabilization Schemes for Evolutionary Convection-Diffusion Equations - Institute Research Grant — IIT Gandhinagar
A Posteriori Error Estimation for Flux Corrected Transport Schemes
Awards & Scholarships
- BMS Phase II Scholarship — Berlin Mathematical School, 2017–2020
- CSIR-UGC NET JRF — All India Rank 28, 2016
- Dr. Gorakh Prasad Scholarship — IIT Roorkee, 2015–2017 · 1st rank in department
- Department of Mathematics Leadership Award — St. Stephen's College, 2015
- INSPIRE Scholarship — Government of India, 2012–2017
Service
- Faculty Advisor — M.Sc. Mathematics, 2028 batch, IIT Gandhinagar
- Web Administrator — Department of Mathematics website, IIT Gandhinagar
- Co-organizer — Foundation Program 2025, IIT Gandhinagar
- Student Representative — Berlin Mathematical School, 2018–2019
Reviewer For
- SIAM Journal on Numerical Analysis
- Journal of Computational and Applied Mathematics
- Journal of Numerical Mathematics
- Journal of Chemical Theory and Computation
- Computer Physics Communications
- Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
- International Journal of Computer Mathematics
- The Journal of Supercomputing
- Mathematical Control and Related Fields
- Multidiscipline Modeling in Materials and Structures
- MathSciNet
People
Research Group
Students and postdocs I supervise or have supervised.
Current Members
- Sarthak Sourav DashPhD · since 2025 Adaptive Finite Elements for Parabolic Problems
Alumni
- Ajeet SinghPostdoc · 2026 Discontinuous Galerkin Methods · now at IIT Delhi
- Aditi TomarPostdoc · 2025 Time-Fractional Differential Equations · now at TU Wien
- Pinki KhatunPostdoc · 2025 Physics-Informed Embedded Neural Networks · now at University of Florence
- Junghoon LeeMaster's · 2023 A Posteriori Error Estimators for Laplace Eigenvalue Problems (Universität Stuttgart)
Talks
Workshops & Conferences
Talks I have given, and minisymposia and conferences I have co-organized.
- Aug 2026WAMIEA 2026 — Advanced Methods in Integral Equations and Their ApplicationsDomain Decomposition Methods for Implicit Solvation Models
- Jul 2026WCCM-APCOM 2026Recent Advancements in a Posteriori Error Estimation for Algebraic Stabilizations
- May 20269th National Finite Element Developers' & FEAST Users' Meet (NAFED 09)Advanced Topics in Finite Element Methods
- Sep 2025ENUMATH 2025Recent Advancements in a Posteriori Error Estimation for Algebraic Stabilizations
- Sep 2025ENUMATH 2025 — Minisymposium: Advances in Numerical Methods for Problems from Fluid Mechanics
- Nov 2024IIT GandhinagarDomain Decomposition Methods for Poisson–Boltzmann Equations
- Oct 2023Universität StuttgartDomain Decomposition Methods for the Poisson–Boltzmann Equations
- May 202393rd GAMM Annual MeetingDomain Decomposition Methods for the Poisson–Boltzmann Equations
- Feb 2023SIAM CSE23Adaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations
- Dec 2022Universität StuttgartOverview of the Domain Decomposition Method for the Linear Poisson–Boltzmann Equations
- Aug 202292nd GAMM Annual MeetingComputation of Forces Arising from the Linear Poisson–Boltzmann Method in the Domain Decomposition Paradigm
- Jul 2022WCCM-APCOM 2022A Residual Based a Posteriori Error Estimator for Algebraic Flux Correction Schemes
- Jul 2022WCCM-APCOM 2022 — Minisymposium: Special Methods in Computational Fluid Mechanics
- Jul 2022Workshop on Numerical Methods and Analysis in CFDAdaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations
- Apr 2022RWTH Aachen UniversityAdaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations
- Mar 202218th Workshop on Numerical Methods for Problems with Layer PhenomenaAdaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations
- Sep 2021Chemnitz Finite Element Symposium 2021Residual Based a Posteriori Error Estimators for Algebraic Flux Correction Schemes
- Aug 2021Bound-Preserving Space and Time Discretizations for Convection-Dominated ProblemsResidual Based a Posteriori Error Estimators for Algebraic Flux Correction Schemes
- Jan 2021RWTH Aachen UniversityNumerical Algorithms for Algebraic Stabilizations of Scalar Convection-Dominated Problems
- Jun 2020ESCO 2020 — 7th International Congress of Computational Engineering and SciencesTowards a Posteriori Error Estimators for Algebraic Flux Correction Schemes
- Feb 20208th BMS Student Conference
- Jun 201928th Biennial Numerical Analysis ConferenceOn Numerical Simulations and a Posteriori Analysis for Algebraic Flux Correction Schemes
- Jun 2019MAFELAP 2019On Numerical Simulations and a Posteriori Analysis for Algebraic Flux Correction Schemes
- Dec 201813th International Workshop on Variational Multiscale and Stabilized Finite ElementsInvestigation of Different Solvers for Nonlinear Algebraic Stabilizations of Convection-Diffusion Equations
- Jun 2018BAIL 2018 — International Conference on Boundary and Interior LayersStudy of Iterative Methods for Nonlinear AFC Discretizations on Convection-Diffusion Equations
Code
Software
Packages I have developed or co-developed.
ddX
Fortran · Domain Decomposition for Continuum Solvation Models
- Developed the ddLPB (linear Poisson–Boltzmann) module
- Co-developed the general framework
ParMooN
C++ · Parallel Mathematics and Object-Oriented Numerics
- Developed the algebraic flux correction package for steady and time-dependent problems
- Co-developed the a posteriori estimator package
Join
Openings
There are no funded openings in my group at the moment, but I am happy to support strong candidates who bring their own funding.
Postdoctoral Researchers
If you have your own funding (e.g. NBHM, ANRF NPDF) or would like help applying, write to me. Possible directions:
- Computational Fluid Dynamics — efficient solvers and mixed formulations of convection-diffusion
- Data Science — eigenvalue problems
- Computational Chemistry — iterative analysis of domain decomposition methods
PhD Students
No open position right now. Prospective students need their own funding, e.g. CSIR/UGC JRF, GATE, NBHM, or INSPIRE. If you'd like to discuss research areas and scope, send me an email.
Off the Clock
Miscellaneous
Books I recommend, and a few things I enjoy outside mathematics.
Numerical Analysis
- Numerical Analysis — Burden & Faires · all of introductory numerical analysis
- Numerical Solution of PDEs by the Finite Element Method — Claes Johnson · the best introduction to FEM
- Finite Elements: Theory and Algorithms — Ganesan & Tobiska · theory and implementation
- Theory and Practice of Finite Elements — Ern & Guermond · advanced FEM
- A Posteriori Error Estimation in Finite Element Analysis — Ainsworth & Oden · adaptive FEM
- Essential Partial Differential Equations — Griffiths, Dold & Silvester · finite differences
Functional Analysis
- Sobolev Spaces — Adams & Fournier
- Topics in Functional Analysis and Applications — S. Kesavan · what FEM needs
Computational Fluid Dynamics
- Robust Numerical Methods for Singularly Perturbed Differential Equations — Roos, Stynes & Tobiska
- Finite Element Methods for Incompressible Flow Problems — Volker John
- Monotone Discretizations for Elliptic Second Order PDEs — Barrenechea, John & Knobloch
Comics & Reading
- The Dark Knight Returns — Frank Miller
- Batman: New 52 — Scott Snyder
- Batman: The Killing Joke — Alan Moore
- JLA: Tower of Babel — Mark Waid
- Identity Crisis — Brad Meltzer
- Doctor Strange: The Oath — Brian K. Vaughan
- Blink — Malcolm Gladwell
On Screen
- Death Note · anime
- Naruto · anime
- Dark
- Peacemaker
- Stranger Things
- Kim's Convenience
- Lanterns
Otherwise
A lifelong football fan who supports Chelsea FC. I play trading card games, mostly Magic: The Gathering and Flesh and Blood, and I listen to a lot of podcasts; two all-time favourites are 44Two and TISS.
Contact
Get in Touch
Feel free to write to me. If I don't respond, don't feel guilty about sending a reminder.
- abhinav.jha@iitgn.ac.in
- Office
- Department of Mathematics
Indian Institute of Technology Gandhinagar
Palaj, Gujarat, India