相关论文: Stability and Functional Superconvergence of Narro…

Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based on a common framework. Conditions under which the SBP-SAT…

The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…

We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order…

This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) finite-difference operators. More precisely, the focus is on…

Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to…

The comprehensive generalization of summation-by-parts of Del Rey Fern\'andez et al.\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of…

The paper presents high-order accurate, energy-, and entropy-stable discretizations constructed from summation-by-parts (SBP) operators. Notably, the discretizations assemble global SBP operators and use continuous solutions, unlike…

This work focuses on multidimensional summation-by-parts (SBP) discretizations of linear elliptic operators with variable coefficients. We consider a general SBP discretization with dense simultaneous approximation terms (SATs), which serve…

High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of…

We employ the summation-by-parts (SBP) framework to extend the recent domain-of-dependence (DoD) stabilization for cut cells to linear kinetic models in diffusion scaling. Numerical methods for these models are challenged by increased…

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid…

Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developing stable, high-order accurate numerical methodologies for…

We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves to mitigate outer boundary effects and, in the future, will…

The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine…

Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. This property can be useful in constructing energy-stable discretizations of partial differential vequations. SBP operators are defined by a…

The scalar, one-dimensional advection equation and heat equation are considered. These equations are discretized in space, using a finite difference method satisfying summation-by-parts (SBP) properties. To impose the boundary conditions,…

We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed by splitting the simplices into quadrilateral or hexahedral…

The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, however, stability and consistency alone do not generally…

By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…

We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numerical discretizations of partial differential equations.…