相关论文: High Order Weighted Extrapolation for Boundary Con…

The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the…

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

We present an improved high-order weighted compact high resolution (WCHR) scheme that extends the idea of weighted compact nonlinear schemes (WCNS's) using nonlinear interpolations in conjunction with compact finite difference schemes for…

In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with non-smooth solution. Two popular finite…

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…

In this paper, we proposed a new boundary condition scheme for the BGK model which has second order accuracy and can be developed to higher accuracy. Numerical tests show that the numerical solutions of the BGK model applied to the new…

This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…

In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…

We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…

In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…

High order numerical methods for networks of hyperbolic conservation laws have recently gained increasing popularity. Here, the crucial part is to treat the boundaries of the single (one-dimensional) computational domains in such a way that…

In material science, image segmentation is of great significance for quantitative analysis of microstructures. Here, we propose a novel Weighted Propagation Convolution Neural Network based on U-Net (WPU-Net) to detect boundary in…

Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…

Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more {system} parameters are not normal, uniform, or closely related…

In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…

In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…

In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…

This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…