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Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods
We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral-element methods (DGSEMS). The use of...
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Partial Newton-Correction Method for Multiple Fixed Points of Semi-linear Differential Operators by Legendre–Gauss–Lobatto Pseudospectral Method
Inspired by several numerical methods for finding multiple solutions, a partial Newton-correction method (PNCM) is proposed to find multiple fixed...
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New Stable Discontinuous Galerkin Methods on Equidistant and Scattered Points
Up to now, we have studied already existing numerical methods, investigated their properties and extended stability conditions in this context....
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Transversely Isotropic Homogeneous Medium with Absorbing Boundary Conditions: Elastic Wave Propagation Using Spectral Element Method
Particle displacements and stresses are calculated for studying elastic wave propagation in a transversely isotropic homogeneous medium. A mesh...
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Admissibility Preserving Subcell Limiter for Lax–Wendroff Flux Reconstruction
Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. We develop a...
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Unified Analysis of Any Order Spectral Volume Methods for Diffusion Equations
In this paper, a new class of spectral volume (SV) methods are proposed, analyzed, and implemented for diffusion equations, with the viscous flux...
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On Kosloff Tal-Ezer least-squares quadrature formulas
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of...
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New Error Bounds for Legendre Approximations of Differentiable Functions
In this paper we present a new perspective on error analysis for Legendre approximations of differentiable functions. We start by introducing a...
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Entropy Stable Galerkin Methods with Suitable Quadrature Rules for Hyperbolic Systems with Random Inputs
In this paper, we investigate hyperbolic systems with random inputs based on generalized polynomial chaos (gPC) approximations, which is one of the...
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A novel class of collocation methods based on the weighted integral form of ODEs
In this work, a novel class of collocation methods for numerical integration of ODEs is presented. Methods are derived from the weighted integral...
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Two-dimensional Jacobi pseudospectral quadrature solutions of two-dimensional fractional Volterra integral equations
In this paper, the author is to introduce the Jacobi pseudospectral quadrature simulation technique for the numerical solutions of two-dimensional...
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Fractional-order shifted Legendre collocation method for solving non-linear variable-order fractional Fredholm integro-differential equations
Fractional differential equations have been adopted for modeling many real-world problems, namely those appearing in biological systems since they...
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Pseudospectral quadrature simulation technique for spatio-temporally parabolic multi-dimensional nonlinear fractional evolution equation
The aim of this paper, the author is to introduce the Jacobi pseudospectral quadrature simulation technique for the multi-dimensional nonlinear...
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Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods
We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG...
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Spectral collocation methods for fractional multipantograph delay differential equations*
In this paper, we propose and analyze a spectral collocation method for the numerical solutions of fractional multipantograph delay differential...
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Convergence analysis for delay Volterra integral equation
In this article we use Chebyshev spectral collocation method to deal with the Volterra integral equation which has two kinds of delay items. We use...
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An Entropy Stable Discontinuous Galerkin Method for the Two-Layer Shallow Water Equations on Curvilinear Meshes
We present an entropy stable nodal discontinuous Galerkin spectral element method (DGSEM) for the two-layer shallow water equations on two...
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Quadrature Rules
Both finite element and finite volume methods are based on integral expressions, and these are usually computed using numerical quadrature. Computer...
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Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation
In the context of preserving stationary states, e.g. lake at rest and moving equilibria, a new formulation of the shallow water system, called flux...
