\(hp\) submeshing via non-conforming finite element methods
type: Item
instance of: scholarly article
title: \(hp\) submeshing via non-conforming finite element methods
zbMATH Open document ID: 0971.65101
DOI: 10.1016/S0045-7825(99)00414-4
author: Padmanabhan Seshaiyer
author: Manil Suri
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2001-03-19T00:00:00Z
review text: The mixed boundary value problem in a bounded polygonal domain \(\Omega\) in \({\mathbb R}^2\) is considered for the Poisson equation. The authors give a review of grid methods with discontinuous approximations (mortar element methods) and pay special attention to the analysis of two variants of non-conforming finite element methods with piecewise polynomial approximations on triangular cells and different ways to approximate the continuity of the function on the cutting line (interface). Estimates of convergence are suggested which depend on the grid parameter and degree of used polynomials. The authors present numerical results in details and conclude the paper by a desription of possible generalization for three-dimensional domains. There are remarks about optimality of the methods ``what is meant that the method should perform as well as the conforming method'', but it is clear that it can not take the place since approximations do not be belong to the original energy space. Besides, the correctness of approximating problems is rather weak since the constant in the inf-sup condition (3.2) might tend to 0.
reviewed by: Evgeniĭ Dyakonov
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 1538644
zbMATH Keywords: elliptic problems
zbMATH Keywords: non-conforming finite element methods
zbMATH Keywords: \(hp\) submeshing
zbMATH Keywords: Poisson equation
zbMATH Keywords: mortar element methods
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1538644