14 citations · 33 across the 12 of their papers we have counts for
12 papers
Structure-Preserving Discontinuous Galerkin Methods for Stochastic Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. In many practical appl…
Energy Stable and Structure-Preserving Algorithms for the Stochastic Galerkin System of 2D Shallow Water Equations
Yekaterina Epshteyn, Akil Narayan, Yinqian Yu
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering ph…
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonline…
Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior
Yekaterina Epshteyn, Chang Liu, Chun Liu +1
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameter…
Local well-posedness of a nonlinear Fokker-Planck model
Yekaterina Epshteyn, Chang Liu, Chun Liu +1
Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker-Planck equations are powerful mathematic…
Non-Dissipative and Structure-Preserving Emulators via Spherical Optimization
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such a…
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
Stochastic Galerkin formulations of the two-dimensional shallow water systems parameterized with random variables may lose hyperbolicity, and hence change the nature of the origina…
Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
Yekaterina Epshteyn, Thuong Nguyen
In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical…
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
Dihan Dai, Yekaterina Epshteyn, Akil Narayan
A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve hyperbolicity of the original system. In this work, we develop hyper…
Difference Potentials Method for Models with Dynamic Boundary Conditions and Bulk-Surface Problems
Yekaterina Epshteyn, Qing Xia
In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phe…
Efficient Numerical Algorithms based on Difference Potentials for Chemotaxis Systems in 3D
Yekaterina Epshteyn, Qing Xia
In this work, we propose efficient and accurate numerical algorithms based on Difference Potentials Method for numerical solution of chemotaxis systems and related models in 3D. Th…
High-order numerical methods for 2D parabolic problems in single and composite domains
Gustav Ludvigsson, Kyle R. Steffen, Simon Sticko +4
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains wi…