Performance of nonconforming spectral element method for Stokes problems
نویسندگان
چکیده
A nonconforming spectral element method for the Stokes problem on nonsmooth domains has been proposed in Mohapatra et al. (J Comput Appl Math 372:112696, 2020). The main focus of this article is to study performance problems smooth curvilinear and with mixed boundary conditions. Various test cases are considered including generalized $${\mathbb {R}}^{2}$$ {R}}^{3}$$ verify exponential accuracy method.
منابع مشابه
A Convergent Nonconforming Finite Element Method for Compressible Stokes Flow
We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The velocity (momentum) equation is approximated by a finite element method on div–curl form using the nonconforming Crouzeix– Raviart space. Our main result is that...
متن کاملNonconforming h - p spectral element methods for elliptic problems
In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconform-ing spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a we...
متن کاملA Nonconforming Generalized Finite Element Method for Transmission Problems
We obtain “quasi-optimal rates of convergence” for transmission (interface) problems on domains with smooth, curved boundaries using a non-conforming Generalized Finite Element Method (GFEM). More precisely, we study the strongly elliptic problem Pu := − ∑ ∂j(A ∂iu) = f in a smooth bounded domain Ω with Dirichlet boundary conditions. The coefficients Aij are piecewise smooth, possibly with jump...
متن کاملParallel Implementation of the Spectral Element Method with Nonconforming Mesh
The Nonconforming Spectral Element Method (NSEM) solves PDEs in complex geometries with high accuracy, however, it is an expensive method. Since parallel computation is eeective in decreasing CPU time, a parallel algorithm for the NSEM is presented. Implementations on SGI Power Challenge using MPI are evaluated in terms of measured speedup and parallel eeciency for schemes of one element and mu...
متن کاملA stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations
Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier–Stokes equations, along with a piecewiseconstant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational & Applied Mathematics
سال: 2022
ISSN: ['1807-0302', '2238-3603']
DOI: https://doi.org/10.1007/s40314-022-01863-w