Research

My research interests are in numerical mathematics, with an emphasis on the stability of numerical methods for PDEs and on bridging theory with applications, including metal casting, brain fluid dynamics, and ice sheet modeling.

Research interests (current):

  • Time-step size estimation and stability constraints for multiphysics problems.
  • Stability and well-posedness of PDEs constrained by data on low-dimensional interior sets (points, curves, surfaces, sparse sensor locations).

Research interests (earlier):

  • Development of a theoretical framework for the stability analysis of kernel-based methods for elliptic and time-dependent hyperbolic PDEs.
  • Numerical stability and robustness in computational ice sheet dynamics.
  • Biomechanical simulation of the thoracic diaphragm.

Publications

  1. Stability analysis of the free-surface Stokes problem and an unconditionally stable explicit scheme. Preprint. 2025
  2. Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions. BIT Numerical Mathematics. 2025.
  3. Weak form Shallow Ice Approximation models with an improved time step restriction. Journal of Glaciology. 2025.
  4. Stability estimates for radial basis function methods applied to linear scalar conservation laws. Applied Mathematics and Computation, 2025.
  5. An RBF partition of unity method for geometry reconstruction and PDE solution in thin structures. Preprint, 2024.
  6. Meshfree RBF–FD methods for numerical simulation of PDE problems. Journal of Physics, 2024.
  7. Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws. Journal of Scientific Computing, 2022.
  8. An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations. Journal of Computational Physics, 2022.
  9. A least squares radial basis function finite difference method with improved stability properties. SIAM Journal on Scientific Computing, 2021.
  10. An unfitted RBF-FD method in a least-squares setting for elliptic PDEs on complex geometries. Journal of Computational Physics, 2021.
  11. A first meshless approach to simulation of the elastic behaviour of the diaphragm. Springer, Lecture notes in Computational Science and Engineering, 2020.