4 papers
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…
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…