Journal Publications (by Research Area)

A Posteriori Error Analysis & Adaptive Finite Element Methods

10. N. Shravani, G. M. M. Reddy, and M. Vynnycky, A posteriori error estimates for the Crank–Nicolson method: application to parabolic partial differential equations subject to a Robin boundary condition with small randomness, J. Sci. Comput., 104 (2025), pp. 1–36.

9. N. Shravani, G. M. M. Reddy, and Amiya K. Pani, Anisotropic a posteriori error analysis for the two-step backward differentiation formula for parabolic integro-differential equations, J. Sci. Comput., 93 (2022), pp. 1–26.

8. G. M. M. Reddy, Fully discrete a posteriori error estimates for parabolic integro-differential equations using the two-step backward differentiation formula, BIT Numer. Math., 62 (2022), pp. 1–27.

7. G. M. M. Reddy, R. K. Sinha, and J. A. Cuminato, A posteriori error analysis of the Crank–Nicolson finite element method for parabolic integro-differential equations, J. Sci. Comput., 79 (2019), pp. 414–441.

6. J. S. Gupta, R. K. Sinha, G. M. M. Reddy, and J. Jain, A posteriori error analysis of the Crank–Nicolson finite element method for linear parabolic interface problems: a reconstruction approach, J. Comput. Appl. Math., 340 (2018), pp. 173–190.

5. J. S. Gupta, R. K. Sinha, G. M. M. Reddy, and J. Jain, New Clement-type interpolation inequalities and a posteriori error estimates for linear parabolic interface problems, Numer. Methods Partial Differ. Equ., 33 (2017), pp. 570–598.

4. J. S. Gupta, R. K. Sinha, G. M. M. Reddy, and J. Jain, A posteriori error analysis of the two-step backward differentiation formula finite element approximation for parabolic interface problems, J. Sci. Comput., 69 (2016), pp. 406–429.

3. G. M. M. Reddy and R. K. Sinha, On the Crank–Nicolson anisotropic a posteriori error analysis for parabolic integro-differential equations, Math. Comp., 85 (2016), pp. 2365–2390.

2. G. M. M. Reddy and R. K. Sinha, The backward Euler anisotropic a posteriori error analysis for parabolic integro-differential equations, Numer. Methods Partial Differ. Equ., 32 (2016), pp. 1309–1330.

1. G. M. M. Reddy and R. K. Sinha, Ritz–Volterra reconstructions and a posteriori error analysis of the finite element method for parabolic integro-differential equations, IMA J. Numer. Anal., 35 (2015), pp. 341–371.

Inverse Problems

7. G. M. M. Reddy, P. Nanda, and M. Vynnycky, A decompositional approach for two-dimensional, two-phase, nonlinear inverse Stefan problems using the method of fundamental solutions, Stud. Appl. Math., 156 (2026), Article e70184.

6. P. Nanda, G. M. M. Reddy, and M. Vynnycky, Inverse two-phase nonlinear Stefan and Cauchy–Stefan problems: a phase-wise approach, Comput. Math. Appl., 123 (2022), pp. 216–226.

5. P. Nanda and G. M. M. Reddy, Efficient numerical solution of one-phase linear inverse Stefan and Cauchy–Stefan problems in two dimensions: a posteriori error control, Stud. Appl. Math., 148 (2022), pp. 1563–1585.

4. G. M. M. Reddy, P. Nanda, M. Vynnycky, and J. A. Cuminato, Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization, Appl. Math. Comput., 409 (2021), Article 12640.

3. G. M. M. Reddy, P. Nanda, M. Vynnycky, and J. A. Cuminato, An adaptive boundary algorithm for the reconstruction of boundary and initial data using the method of fundamental solutions for the inverse Cauchy–Stefan problem, Comput. Appl. Math., 40 (2021), pp. 1–26.

2. G. M. M. Reddy, M. Vynnycky, and J. A. Cuminato, An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem, J. Comput. Appl. Math., 349 (2019), pp. 21–40.

1. G. M. M. Reddy, M. Vynnycky, and J. A. Cuminato, On efficient reconstruction of boundary data with optimal placement of source points in the method of fundamental solutions: application to inverse Stefan problems, Inverse Probl. Sci. Eng., 26 (2018), pp. 1249–1279.

AI & Machine Learning

1. A. Ogueda, L. Lakshminarayanan, G. M. M. Reddy, and P. Seshaiyer, Efficient and scalable Galerkin neural networks for multiphysics problems via domain decomposition, Machine Learning: Computational Science and Engineering, 2 (2026), Article 7.

Conference Proceedings

1. A. Ogueda, P. Seshaiyer, M. Raissi, L. Lakshminarayanan, and G. M. M. Reddy, Galerkin Neural Networks as a meshless method for solving PDEs, Joint Mathematics Meetings, American Mathematical Society, 2026.

Software