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Thanks to the singularity of the solution of linear subdiffusion problems, most time-stepping methods on uniform meshes can result in $O(\tau)$ accuracy where $\tau$ denotes the time step. The present work aims to discover the reason why…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. We develop a subcell based limiter by blending LWFR with a lower order scheme, either first order finite…
Typically when a semi-discrete approximation to a partial differential equation (PDE) is constructed a discretization of the spatial operator with a truncation error $\tau$ is derived. This discrete operator should be semi-bounded for the…
The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…
This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…
Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
In this paper we propose and analyze a (temporally) third order accurate exponential time differencing (ETD) numerical scheme for the no-slope-selection (NSS) equation of the epitaxial thin film growth model, with Fourier pseudo-spectral…
We propose an improved version of the PAMPA algorithm where the solution is sought as globally continuous. The scheme is locally conservative, and there is no mass matrix to invert. This method had been developed in a series of papers, see…
The Truncated conformal space approach (TCSA) is a numerical technique for finding finite size spectrum of Hamiltonians in quantum field theory described as perturbations of conformal field theories. The truncation errors of the method have…
In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for…
A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier-Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained…
A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In this triple junction, conditions are imposed on the angles at…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
In this work, we introduced a class of nonlocal models to accurately approximate the Poisson model on manifolds that are embedded in high dimensional Euclid spaces with Dirichlet boundary. In comparison to the existing nonlocal Poisson…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…