Variational Methods for BEM

As we all know, variational methods and formulations are basic for a big variety of problems in mechanics [12]. Their exploitation in connection with finite element approximation has created some of the most powerful algorithms in computational mechanics, the finite element methods.

[1]  Douglas N. Arnold,et al.  On the asymptotic convergence of collocation methods , 1983 .

[2]  Reinhold Schneider,et al.  Spline approximation methods for multidimensional periodic pseudodifferential equations , 1992 .

[3]  J. Planchard,et al.  Une méthode variationnelle d’éléments finis pour la résolution numérique d’un problème extérieur dans $\mathbf {R}^3$ , 1973 .

[4]  Ian H. Sloan,et al.  A Quadrature-Based Approach to Improving the Collocation Method for Splines of Even Degree , 1989 .

[5]  Wolfgang L. Wendland,et al.  On the asymptotic convergence of collocation methods with spline functions of even degree , 1985 .

[6]  Wolfgang L. Wendland,et al.  Finite Element and Boundary Element Techniques from Mathematical and Engineering Point of View , 1988 .

[7]  O. D. Kellogg.  Foundations of potential theory , 1934 .

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

[9]  Martin Costabel,et al.  Principles of boundary element methods , 1987 .

[10]  A. Maue,et al.  Zur Formulierung eines allgemeinen Beugungs-problems durch eine Integralgleichung , 1949 .

[11]  Jukka Saranen,et al.  The convergence of even degree spline collocation solution for potential problems in smooth domains of the plane , 1988 .

[12]  Franco Brezzi,et al.  On the coupling of boundary integral and finite element methods , 1979 .

[13]  M. De.  Handbuch der Physik , 1957 .

[14]  D. Arnold,et al.  The convergence of spline collocation for strongly elliptic equations on curves , 1985 .

[15]  Reinhold Schneider,et al.  Error analysis of a boundary element collocation method for a screen problem in , 1992 .

[16]  W. Wendland,et al.  A finite element method for some integral equations of the first kind , 1977 .

[17]  David A. H. Jacobs,et al.  The State of the Art in Numerical Analysis. , 1978 .

[18]  F. Brezzi,et al.  On the coupling of boundary integral and finite element methods , 1979 .

[19]  Ian H. Sloan,et al.  A quadrature-based approach to improving the collocation method , 1988 .

[20]  Reinhold Schneider,et al.  Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations , 1990 .

[21]  C. Brebbia,et al.  Boundary Elements IX , 1987 .

[22]  S. Prössdorf,et al.  A Finite Element Collocation Method for Singular Integral Equations , 1981 .

[23]  G. Fichera.  Existence Theorems in Elasticity , 1973 .

[24]  Gabriel N. Gatica,et al.  The Coupling of Boundary Element and Finite Element Methods for a Nonlinear Exterior Boundary Value Problem , 1989 .

[25]  Wolfgang L. Wendland,et al.  The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations , 1985 .

[26]  G. Fichera.  Boundary Value Problems of Elasticity with Unilateral Constraints , 1973 .

[27]  On nonlinear mixed boundary value problems for second order elliptic differential equations on domains with corners , 1980 .

[28]  E. Sternberg,et al.  Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , 1980 .

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

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

[31]  Domain decomposition method for magnetostatics nonlinear problems in combined formulation , 1990 .

[32]  J. Grannell.  On Simplified Hybrid Methods for Coupling of Finite Elements and Boundary Elements , 1987 .