Adaptive coupling of boundary elements and finite elements

Nous presentons un procede adaptatif pour coupler des methodes d'elements finis et d'elements frontiere pour des problemes d'interface lineaires ou non lineaires. Une estimation d'erreur a posteriori est obtenue. Des exemples numeriques confirment que ce procede donne de bons maillages, menant a des methodes numeriques efficaces.

[1]  Dieter Gaier,et al.  Integralgleichungen erster Art und konforme Abbildung , 1976 .

[2]  Norbert Heuer,et al.  On the h-p version of the boundary element method for Symm's integral equation on polygons , 1993 .

[3]  Carsten Carstensen,et al.  Interface problem in holonomic elastoplasticity , 1993 .

[4]  Carsten Carstensen,et al.  Adaptive Boundary Element Methods for Some First Kind Integral Equations , 1996 .

[5]  Kenneth Eriksson,et al.  An adaptive finite element method for linear elliptic problems , 1988 .

[6]  Carsten Carstensen,et al.  Coupling of FEM and BEM for a nonlinear interface problem: the h-p version , 1995 .

[7]  P. Clément.  Approximation by finite element functions using local regularization , 1975 .

[8]  R. Verfürth.  A posteriori error estimates for nonlinear problems: finite element discretizations of elliptic equations , 1994 .

[9]  E. Rank.  Adaptive Boundary Element Methods (Invited contribution) , 1987 .

[10]  H. Beckert,et al.  J. L. Lions and E. Magenes, Non‐Homogeneous Boundary Value Problems and Applications, II. (Die Grundlehren d. Math. Wissenschaften, Bd. 182). XI + 242 S. Berlin/Heidelberg/New York 1972. Springer‐Verlag. Preis geb. DM 58,— , 1973 .

[11]  M. Costabel,et al.  Coupling of Finite Elements and Boundary Elements for Transmission Problems of Elastic Waves in R3 , 1988 .

[12]  Martin Costabel,et al.  Coupling of finite and boundary element methods for an elastoplastic interface problem , 1990 .

[13]  Martin Costabel,et al.  Boundary Integral Operators on Lipschitz Domains: Elementary Results , 1988 .

[14]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[15]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[16]  Kenneth Eriksson,et al.  Adaptive finite element methods for parabolic problems. I.: a linear model problem , 1991 .

[17]  Ernst P. Stephan,et al.  An augmented galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems , 1984 .

[18]  I. Babuska,et al.  A-Posteriori Error Estimates and Adaptive Techniques for the Finite Element Method. , 1981 .

[19]  Wolfgang L. Wendland,et al.  On Asymptotic Error Estimates for Combined Bem and Fem , 1988 .

[20]  Gabriel N. Gatica,et al.  On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2 , 1992 .

[21]  Claes Johnson,et al.  Adaptive finite element methods in computational mechanics , 1992 .

[22]  Ernst P. Stephan,et al.  On the h-, p- and h-p versions of the boundary element method-numerical results , 1990 .

[23]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[24]  A. Stroud,et al.  Gaussian quadrature formulas , 1966 .

[25]  Ian H. Sloan,et al.  The Galerkin Method for Integral Equations of the First Kind with Logarithmic Kernel: Theory , 1988 .

[26]  Martin Costabel,et al.  Symmetric Methods for the Coupling of Finite Elements and Boundary Elements (Invited contribution) , 1987 .

[27]  Rüdiger Verfürth.  A Posteriori Error Estimates for Non-Linear Problems , 1994 .

[28]  E. Rank,et al.  Adaptive boundary element methods , 1987 .

[29]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[30]  Martin Costabel,et al.  A direct boundary integral equation method for transmission problems , 1985 .

[31]  Wolfgang L. Wendland,et al.  Adaptive boundary element methods for strongly elliptic integral equations , 1988 .