A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion--Reaction Problems
In this article, a new weak Galerkin finite element method is introduced to solve convection-
diffusion--reaction equations in the convection dominated regime. Our method is highly …
diffusion--reaction equations in the convection dominated regime. Our method is highly …
An interface-fitted mesh generator and virtual element methods for elliptic interface problems
A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-
structured interface-fitted mesh in two and three dimensions quickly is developed in this …
structured interface-fitted mesh in two and three dimensions quickly is developed in this …
INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems
S Wu, B Lu - Journal of Computational Physics, 2022 - Elsevier
Abstract Machine learning has been successfully applied to various fields in computational
science and engineering. In this paper, we propose interfaced neural networks (INNs) to …
science and engineering. In this paper, we propose interfaced neural networks (INNs) to …
Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms
Ş Toprakseven, P Zhu - Applied Mathematics and Computation, 2023 - Elsevier
A weak Galerkin finite element method is proposed for solving singularly perturbed
problems with two parameters. A robust uniform optimal convergence has been proved in …
problems with two parameters. A robust uniform optimal convergence has been proved in …
Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges
In this article, we discuss and analyze a conforming virtual element discretization with
boundary stabilization term proposed in Brenner and Sung (2018)[30](suitable for small …
boundary stabilization term proposed in Brenner and Sung (2018)[30](suitable for small …
Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts
The conjugate heat transfer problem is found in non-isothermal physical systems that
involve thermodynamic processes between materials that are thermally coupled through …
involve thermodynamic processes between materials that are thermally coupled through …
Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems
M Dehghan, M Abbaszadeh - Computer Methods in Applied Mechanics …, 2018 - Elsevier
The main aim of the current paper is to propose a new truly meshless numerical technique to
solve the one-and two-dimensional elliptic interface problems. The employed meshless …
solve the one-and two-dimensional elliptic interface problems. The employed meshless …
Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions
In this paper, we consider the weak Galerkin finite element approximations of second order
linear parabolic problems in two dimensional convex polygonal domains under the low …
linear parabolic problems in two dimensional convex polygonal domains under the low …
A stabilizer free weak Galerkin finite element method with supercloseness of order two
The weak Galerkin (WG) finite element method is an effective and flexible general numerical
technique for solving partial differential equations. A simple WG finite element method is …
technique for solving partial differential equations. A simple WG finite element method is …
Solving parametric elliptic interface problems via interfaced operator network
Learning operators mapping between infinite-dimensional Banach spaces via neural
networks has attracted a considerable amount of attention in recent years. In this paper, we …
networks has attracted a considerable amount of attention in recent years. In this paper, we …