The coupling of boundary integral and finite element methods for nonmonotone nonlinear problems∗

DOI10.1080/01630569208816490zbMath0764.65070OpenAlexW1973673263MaRDI QIDQ4029154

Gabriel N. Gatica, George C. Hsiao

Publication date: 7 March 1993

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569208816490

zbMATH Keywords

convergencefinite element methodboundary integral equationsGalerkin approximationsnon-monotone nonlinear exterior boundary value problemsnonlinear \(A\)-proper mappings

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items

On the coupling of boundary integral and finite element methods with nonlinear transmission conditions, A boundary-field equation method for a nonlinear exterior elasticity problem in the plane, On the numerical solution of linear exterior problems via the uncoupling method, The coupling of boundary integral and finite element methods for the exterior steady Oseen problem, Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems, Finite element schemes for non-linear problems in infinite domains, Further developments on boundary-field equation methods for nonlinear transmission problems, Variational formulations of transmission problems via FEM, BEM and DtN mappings, Dirichlet-to-Neumann maps for unbounded wave guides, Finite-element solution of nonlinear time-dependent exterior wave problems, A unified variational approach to domain-based computation of exterior problems of time-harmonic acoustics, Optimal local non-reflecting boundary conditions

Cites Work

• Unnamed Item
• The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem
• Fredholm alternatives for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems
• On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in \(\mathbb{R}^ 2\)
• A convergent finite element formulation for transonic flow
• On the approximation-solvability of nonlinear equations
• Finite elements for transonic potential flows
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• On the approximation-solvability of equations involving 𝐴-proper and pseudo-𝐴-proper mappings
• Coupling of Finite and Boundary Element Methods for an Elastoplastic Interface Problem