Related papers: A non-separable progressive multivariate WENO-$2r$…

We investigate a weighted Multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in~[Lemaire-Pag\`es, 2013] for regular Monte Carlo simulation. In a…

We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…

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, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of…

Recently, the targeted ENO (TENO) schemes give a novel framework to keep optimal high-order spatial reconstruction wherever discontinuity is deemed to be vanished, including at smooth critical points, and to avoid oscillations by completely…

Including polynomials with small degree and stencil when designing very high order reconstructions is surely beneficial for their non oscillatory properties, but may bring loss of accuracy on smooth data unless special care is exerted. In…

A new scheme for communication between overset grids using subcells and Weighted Essentially Non Oscillatory (WENO) reconstruction for two-dimensional problems has been proposed. The effectiveness of this procedure is demonstrated using the…

We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space-time adaptive mesh refinement (AMR). The resulting…

Although there are many improvements to WENO3-Z that target the achievement of optimal order in the occurrence of the first-order critical point (CP1), they mainly address resolution performance, while the robustness of schemes is of less…

We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…

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…

This paper deals with a new fifth-order weighted essentially non-oscillatory (WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016)…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

The main aim of this work is not to improve any existing non-linear weight but to give a generalized framework for the construction of non-linear weights to get non-oscillatory third order WENO schemes. It is done by imposing necessary…

The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to…

In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first-order…

We propose an alternative reconstruction for weighted essentially non-oscillatory schemes with adaptive order (WENO-AO) for solving hyperbolic conservation laws. The alternative reconstruction has a more concise form than the original…

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…

We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated…