Related papers: High-Order, Stable, And Efficient Pseudospectral M…
This paper extends a new class of positivity-preserving, entropy stable spectral collocation schemes developed for the one-dimensional compressible Navier-Stokes equations in [1,2] to three spatial dimensions. The new high-order schemes are…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme preserves a semi-discrete entropy inequality and remains…
When nonconforming discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme with exact integration does not support such growth. Using…
We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+\beta}$ with $\beta\ge 1$ being a free parameter.…
In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
We revisit the numerical stability of four well-established explicit stochastic integration schemes through a new generic benchmark stochastic differential equation designed to assess asymptotic statistical accuracy and stability…
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…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions with a restricted isometry relation derived from…