Solution of nonlinear elliptic equations with boundary singularities by an integral equation method

DOI10.1016/0021-9991(84)90094-9zbMath0557.65078OpenAlexW2014368212MaRDI QIDQ761783

Mark A. Kelmanson

Publication date: 1984

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(84)90094-9

zbMATH Keywords

boundary integral equationboundary singularitiesintegral equation methodnonlinear boundary conditionsnonlinear elliptic equationsKirchoff transformation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Nonlinear boundary value problems for linear elliptic equations (35J65) Integral representations of solutions to PDEs (35C15) Integral equations with kernels of Cauchy type (45E05)

Related Items

A BIE method for a nonlinear BVP, Annihilation of boundary singularities via suitable Green's functions, A boundary element method for a nonlinear boundary value problem in steady-state heat transfer, On the boundary element method for some nonlinear boundary value problems, A boundary element method for a nonlinear boundary value problem in steady-state heat transfer in dimension three, Multilevel augmentation methods for nonlinear boundary integral equations II: Accelerated quadratures and Newton iterations, Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods, Boundary element methods for potential problems with nonlinear boundary conditions, Integral equation analysis of the driven-cavity boundary singularity, Nonlinear boundary integral equations for harmonic problems, A nonlinear boundary value problem solved by spectral methods, On the collocation method for a nonlinear boundary integral equation, An integral equation justification of the boundary conditions of the driven-cavity problem

Cites Work

• The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method
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• The numerical solution of plane potential problems by improved boundary integral equation methods
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• Modified integral equation solution of viscous flows near sharp corners
• The Optimum Addition of Points to Quadrature Formulae
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