Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems

DOI10.1080/00036819608840495zbMath0865.65077OpenAlexW1964862562WikidataQ58299577 ScholiaQ58299577MaRDI QIDQ5691464

Wolfgang L. Wendland, Gabriel N. Gatica

Publication date: 5 February 1997

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819608840495

zbMATH Keywords

existenceuniquenessdomain decompositionmonotone operatorsboundary integral methodsGalerkin schemesinf-sup conditionsnonlinear magnetic fieldtwo-dimensional Laplacianlinear constrained variational problemslinear and nonlinear elliptic boundary value problemscoupling of mixed finite element

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solutions to equations with nonlinear operators (65J15) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (32)

A dual-mixed approximation for a huber regularization of generalized \(p\)-Stokes viscoplastic flow problems ⋮ A fully-mixed finite element method for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity ⋮ On the coupling of boundary integral and finite element methods with nonlinear transmission conditions ⋮ An A-Posteriori Error estimate for the coupling of BEM and mixed-FEM ⋮ An augmented mixed-primal finite element method for a coupled flow-transport problem ⋮ Coupling of finite element and boundary integral methods for electromagnetic scattering in a two-layered medium ⋮ Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity ⋮ An augmented fully-mixed finite element method for a coupled flow-transport problem ⋮ A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling ⋮ A priori and a posteriori error analyses of augmented twofold saddle point formulations for nonlinear elasticity problems ⋮ A dual-dual mixed formulation for nonlinear exterior transmission problems ⋮ Primal mixed formulations for the coupling of FEM and BEM. Part I: linear problems ⋮ Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces ⋮ A posteriori error analysis of an augmented mixed method for the Navier-Stokes equations with nonlinear viscosity ⋮ An expanded mixed finite element approach via a dual-dual formulation and the minimum residual method ⋮ A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem ⋮ A FULLY DISCRETE GALERKIN SCHEME FOR A TWO-FOLD SADDLE POINT FORMULATION OF AN EXTERIOR NONLINEAR PROBLEM^* ⋮ A posteriorierror estimates for linear exterior problemsviamixed-FEM and DtN mappings ⋮ Further developments on boundary-field equation methods for nonlinear transmission problems ⋮ An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity ⋮ Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds ⋮ A posteriori error analysis of a fully-mixed formulation for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity ⋮ A FEM-BEM approach for electro-magnetostatics and time-harmonic eddy-current problems ⋮ A new non-augmented and momentum-conserving fully-mixed finite element method for a coupled flow-transport problem ⋮ Variational formulations of transmission problems via FEM, BEM and DtN mappings ⋮ Weak solvability of interior transmission problems via mixed finite elements and Dirichlet-to-Neumann mappings ⋮ Boundary value problems for the Brinkman system with \(L^\infty\) coefficients in Lipschitz domains on compact Riemannian manifolds. A variational approach ⋮ On the numerical analysis of finite element and dirichlet-to-neumann methods for nonlinear exterior transmission problems ⋮ Solvability and Galerkin approximations of a class of nonlinear operator equations ⋮ On the dual-mixed formulation for an exterior Stokes problem ⋮ A posteriori error estimates for a mixed-FEM formulation of a nonlinear elliptic problem ⋮ Conjugate gradient method for dual-dual mixed formulations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coupling of finite elements and boundary elements for some nonlinear interface problems
• The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem
• On the coupling of boundary integral and finite element methods
• A finite element method for exterior interface problems
• General stress analysis method by means of integral equations and boundary elements
• A finite element method for some integral equations of the first kind
• Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics
• On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in \(\mathbb{R}^ 2\)
• Plenary Lectures
• The coupling of boundary integral and finite element methods for the bidimensional exterior steady stokes problem
• Finite Element Methods for Navier-Stokes Equations
• The coupling of bem and fem for the two-dimensional viscous flow problem
• On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady stokes problem
• On the Coupling Boundary Integral and Finite Element Methods for the Exterior Stokes Problem in 3-D
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Mixed and Hybrid Finite Element Methods
• Unified symmetric finite element and boundary integral variational coupling methods for linear fluid–structure interaction
• The coupling of boundary integral and finite element methods for nonmonotone nonlinear problems^∗
• Coupling method for the exterior stationary Navier-Stokes equations
• Nonlinear Field Calculations with Multigrid-Newton Methods
• Analysis of a Fully Discrete Finite Element Method for a Nonlinear Magnetic Field Problem
• Variational Formulations for Coupled BE/FE Methods in Elastostatics
• Coupling of Finite and Boundary Element Methods for an Elastoplastic Interface Problem

This page was built for publication: Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems