9 papers
Geometry-Conforming Finite Element Methods for Interface Problems on Fitted and Unfitted Meshes
Yuanhui Lin, Tao Lin, Xu Zhang +1
We develop an arbitrary-degree geometry-conforming finite element (GC-FE) framework for two-dimensional elliptic boundary value and interface problems on curved domains. Using the…
A time-decoupling scheme for mixed-dimensional poroelastic models with fractures
Dongchun Tang, Linshuang He, Shuyu Sun +1
We propose a locking-free decoupling method for a mixed-dimensional poroelasticity model with fractures. By introducing the total pressure, the fractured Biot system is reformulate…
Pressure-Robust Enriched Galerkin Methods for Navier-Stokes Equations
Chun Song, Minfu Feng
This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces…
Second-order unconditionally stable time-filtered scheme for Cahn-Hilliard-Navier-Stokes system
Xi Li, Chun Song, Haijun Gao +1
In this work, we introduce the time filtering technique to develop several innovative semi-discrete schemes in time for the Cahn-Hilliard-Navier-Stokes (CHNS) system. These schemes…
Optimal convergence analysis of fully discrete SAVs-FEM for the Cahn-Hilliard-Navier-Stokes equations
Haijun Gao, Xi Li, Cheng Wang +1
We construct a fully discrete numerical scheme that is linear, decoupled, and unconditionally energy stable, and analyze its optimal error estimates for the Cahn-Hilliard-Navier-St…
Convergence analysis of decoupled mixed FEM for the Cahn-Hilliard-Navier-Stokes equations
Haijun Gao, Xi Li, Minfu Feng
We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes…
A new decoupled unconditionally stable scheme and its optimal error analysis for the Cahn-Hilliard-Navier-Stokes equations
Haijun Gao, Xi Li, Minfu Feng
We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main p…
Improved physics-informed neural network in mitigating gradient related failures
Pancheng Niu, Yongming Chen, Jun Guo +3
Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. H…
On the conservation properties of the two-level linearized methods for Navier-Stokes equations
Xi Li, Minfu Feng
This manuscript is devoted to investigating the conservation laws of incompressible Navier-Stokes equations(NSEs), written in the energy-momentum-angular momentum conserving(EMAC)…