12 citations · 23 across the 7 of their papers we have counts for
10 papers
Convolution Quadrature with Adaptive History Compression for Variable-Order Fractional Reaction--Diffusion Equations
Pu Yuan, Paul Zegeling
We develop a fully implicit fast method for semilinear variable-order fractional reaction--diffusion equations with periodic fractional diffusion and exponential-transition Scarpi…
Well-posedness and Blow-up in a semilinear heat equation with variable-order Scarpi memory
Pu Yuan, P. A. Zegeling
We study the semilinear heat equation on $\RR^n$, where and the Scarpi order changes exponentially from to , with . We esta…
Wellposedness and dynamics of two types of reaction--nonlocal diffusion systems under the inhomogeneous spectral fractional Laplacian
Pu Yuan, Paul A. Zegeling
Reactio-nonlocal diffusion equations model nonlocal transport and anomalous diffusion by replacing the Laplacian with a fractional power, capturing diffusion mechanisms beyond Brow…
A preconditioned boundary value method for advection-diffusion equations with half Laplacian via spectrum doubling
Pu Yuan, Paul Zegeling, Xian-Ming Gu
In this paper, we study an evolution equation that involves a half-Laplacian operator derived from the Riesz fractional Laplacian, combined with a differential operator \(\mathcal{…
Runge-Kutta symmetric interior penalty discontinuous Galerkin methods for modified Buckley-Leverett equations
Hong Zhang, Yunrui Guo, Weibin Li +1
We present a robust and accurate numerical method to solve the modified Buckley-Leverett equation in two-phase porous media flow with dynamic capillary pressure effect. A symmetric…
Simulation of thin film flows with a moving mesh mixed finite element method
Hong Zhang, Paul A Zegeling
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic m…
A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media
Hong Zhang, Paul Andries Zegeling
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richa…
A numerical study of two-phase flow with dynamic capillary pressure using an adaptive moving mesh method
Hong Zhang, Paul Andries Zegeling
Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow incorporating dynamic capillary pressure. The effects of the dynamic…
A numerical study of two-phase flow models with dynamic capillary pressure and hysteresis
Hong Zhang, Paul Andries Zegeling
Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditi…
Stability and convergence analysis of a class of continuous piecewise polynomial approximations for time fractional differential equations
Han Zhou, Paul Andries Zegeling
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivat…