A nonconforming combined method for solving Laplace's boundary value problems with singularities
type: Item
instance of: scholarly article
title: A nonconforming combined method for solving Laplace's boundary value problems with singularities
zbMATH Open document ID: 0586.65075
DOI: 10.1007/BF01389701
published in: Numerische Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133125
review text: For solving Laplace's boundary value problems with singularities, a nonconforming combined approach of the Ritz-Galerkin method and the finite element method is presented. In this approach, singular functions are chosen to be admissible functions in the part of a solution domain where there exist singularities; and piecewise linear functions are chosen to be admissible functions in the rest of the solution domain. In addition, the admissible functions used here are constrained to be continuous only at the element nodes on the common boundary of both methods. This method is nonconforming; however, the nonconforming effect does not result in larger errors of numerical solutions as long as a suitable coupling strategy is used. In this paper, we will develop such an approach by using a new coupling strategy, which is described as follows: If \(L+1=O(| \ell n h|)\), the average errors of numerical solutions and their generalized derivatives are still O(h), where h is the maximal boundary length of quasiuniform triangular elements in the finite element method, and \(L+1\) is the total number of singular admissible functions in the Ritz-Galerkin method. This coupling relation, \(L+1=O(| \ell n h|)\), is significant because only a few singular functions are required for a good approximation of solutions.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 3940660
zbMATH Keywords: nonconforming combined method
zbMATH Keywords: Laplace equation
zbMATH Keywords: singularities
zbMATH Keywords: Ritz- Galerkin method
zbMATH Keywords: finite element method
author: Zi-Cai Li
MaRDI profile type: Publication
cites work: Q3214109
cites work: Q3049781
cites work: Q4162607
cites work: Q5820676
cites work: An Implicit Matching Principle for Global Element Calculations
cites work: Q3340323
cites work: Q3270785
cites work: Q3925844
cites work: An approach for combining the Ritz-Galerkin and finite element method
cites work: Q3673992
cites work: On the Simplified Hybrid-Combined Method
cites work: Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
cites work: The numerical solutions of interface problems by infinite element method
cites work: Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
cites work: Q4127946
cites work: The use of infinite grid refinements at singularities in the solution of Laplace's equation
cites work: Treatment of harmonic mixed boundary problems by conformal transformation methods
cites work: Q5568224
cites work: On a Method to Subtract off a Singularity at a Corner for the Dirichlet or Neumann Problem
cites work: Q4158078
cites work: The coupling of the finite element method and boundary solution procedures
OpenAlex ID: W2080901934
description: scientific article; zbMATH DE number 3940660