The classical overlapping Schwarz algorithm is here extended to the triangular/tetrahedral spectral element (TSEM) discretization of elliptic problems. This discretization, based on Fekete nodes, is a generalization to nontensorial elements of the tensorial Gauss–Lobatto–Legendre quadrilateral spectral elements (QSEM). The overlapping Schwarz preconditioners are based on partitioning the domain...

This paper is concerned with the hp-version of the finite element method (hp-FEM) to treat a variational inequality that models frictional contact in linear elastostatics. Such an approximation of higher order leads to a nonconforming discretization scheme. We employ Gauss-Lobatto quadrature for the approximation of the nonsmooth frictiontype functional and take the resulting quadrature error i...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 March 2021Accepted: 27 August 2021Published online: 10 February 2022Keywordsspectral element method, Gauss--Lobatto quadrature, superconvergence, wave equation, parabolic equations, linear Schrödinger equationAMS Subject Headings65M60, 65M15, 65M06Publication DataISSN (...

Abstract We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits DG approximation constructed from polynomial basis functions and integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. theoretical discussion re-contextualizes stable results finite difference into setting. Numerical tests verify...

Since proposed in Zhang and Shu (2010) [1], the Zhang–Shu framework has attracted extensive attention motivated many bound-preserving (BP) high-order discontinuous Galerkin finite volume schemes for various hyperbolic equations. A key ingredient is decomposition of cell averages numerical solution into a convex combination values at certain quadrature points, which helps to rewrite as combinati...

A sequence of increasingly refined interpolation grids inside the tetrahedron is proposed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The number of interpolation nodes, N , corresponds to the number of terms in the complete mth-order polynomial expansion with respect to the three tetrahedral barycentric coordinates. The proposed grid is constructed b...

In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching t...