scholarly journals p-refined RBF-FD solution of a Poisson problem

2021 ◽  
Author(s):  
Mitja Jancic ◽  
Jure Slak ◽  
Gregor Kosec
Keyword(s):  
Poisson Problem

Some Estimates for Virtual Element Methods

2017 ◽  
Vol 17 (4) ◽  
pp. 553-574 ◽  
Author(s):  
Susanne C. Brenner ◽  
Qingguang Guan ◽  
Li-Yeng Sung
Keyword(s):  
Error Estimates ◽  
Three Dimensions ◽  
Poisson Problem ◽  
Polyhedral Meshes ◽  
Virtual Element Methods ◽  
Virtual Element

AbstractWe present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions.

The Poisson problem in a domain with a cut

2012 ◽  
Vol 22 (3) ◽  
pp. 204-216
Author(s):  
Yu. N. Subbotin ◽  
N. I. Chernykh
Keyword(s):  
Poisson Problem

scholarly journals Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 281
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Domain Decomposition ◽  
Iterative Algorithm ◽  
Poisson Equation ◽  
Large Scale ◽  
Linear Equations ◽  
Iterative Algorithms ◽  
Computation Time ◽  
Explicit Method ◽  
Computational Process ◽  
Poisson Problem

Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism.

scholarly journals A Resolution of the Poisson Problem for Elastic Plates

2020 ◽  
Vol 236 (3) ◽  
pp. 1593-1676 ◽  
Author(s):  
Francesca Da Lio ◽  
Francesco Palmurella ◽  
Tristan Rivière
Keyword(s):  
Elastic Plates ◽  
Poisson Problem

scholarly journals Bridging the hybrid high-order and virtual element methods

2020 ◽  
Author(s):  
Simon Lemaire
Keyword(s):  
High Order ◽  
Virtual Space ◽  
Approximation Properties ◽  
Virtual Spaces ◽  
Local Polynomial ◽  
Poisson Problem ◽  
Virtual Element Methods ◽  
Dimension 2 ◽  
Virtual Element ◽  
Polytopal Meshes

Abstract We present a unifying viewpoint on hybrid high-order and virtual element methods on general polytopal meshes in dimension $2$ or $3$, in terms of both formulation and analysis. We focus on a model Poisson problem. To build our bridge (i) we transcribe the (conforming) virtual element method into the hybrid high-order framework and (ii) we prove $H^m$ approximation properties for the local polynomial projector in terms of which the local virtual element discrete bilinear form is defined. This allows us to perform a unified analysis of virtual element/hybrid high-order methods, that differs from standard virtual element analyses by the fact that the approximation properties of the underlying virtual space are not explicitly used. As a complement to our unified analysis we also study interpolation in local virtual spaces, shedding light on the differences between the conforming and nonconforming cases.

The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials

2019 ◽  
Vol 19 (3) ◽  
pp. 645-661 ◽  
Author(s):  
Yi Zhang ◽  
Varun Jain ◽  
Artur Palha ◽  
Marc Gerritsma
Keyword(s):  
Test Problem ◽  
Exponential Convergence ◽  
Mixed Formulation ◽  
Curvilinear Coordinates ◽  
Poisson Problem ◽  
Set Up

AbstractIn this paper, we will use algebraic dual polynomials to set up a discrete Steklov–Poincaré operator for the mixed formulation of the Poisson problem. The method will be applied in curvilinear coordinates and to a test problem which contains a singularity. Exponential convergence of the trace variable in {H^{1/2}}-norm will be shown.

scholarly journals A Relaxed Kačanov iteration for the p-poisson problem

2020 ◽  
Vol 145 (1) ◽  
pp. 1-34
Author(s):  
L. Diening ◽  
M. Fornasier ◽  
R. Tomasi ◽  
M. Wank
Keyword(s):  
Poisson Problem
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