On the Convergence of the p-Version of the Boundary Element Galerkin Method.

Abstract : The authors consider various physical problems which may be formulated in terms of integral equations of the first kind, including the two-dimensional screen Neumann and Dirichlet problems in acoustics (and crack problems in elasticity). Sharp regularity results for the solutions are available for these problems. Proven is the convergence of the p-version for some Galerkin boundary element schemes based on the integral equation formulations. It is shown that the rate of convergence obtained by our method is twice that for the usual h-version.

[1]  B. Guo,et al.  The hp version of the finite element method Part 1 : The basic approximation results , 2022 .

[2]  Martin Costabel,et al.  Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation , 1985 .

[3]  Ernst P. Stephan,et al.  Remarks to Galerkin and least squares methods with finite elements for general elliptic problems , 1976 .

[4]  Ernst P. Stephan,et al.  A hypersingular boundary integral method for two-dimensional screen and crack problems , 1990 .

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

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

[7]  Ernst P. Stephan,et al.  Boundary Integral Equations for Mixed Boundary Value Problems in R3 , 1987 .

[8]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Constraint Boundary Conditions. , 1988 .

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

[10]  Manil Suri,et al.  The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method , 1989 .

[11]  W. Wendland.  Boundary Element Methods and Their Asymptotic Convergence , 1983 .

[12]  E. Alarćon,et al.  Hierarchical boundary elements , 1985 .

[13]  W. Wendland,et al.  An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc , 1985 .

[14]  I. Babuska,et al.  Rairo Modélisation Mathématique Et Analyse Numérique the H-p Version of the Finite Element Method with Quasiuniform Meshes (*) , 2009 .

[15]  Stefan Hildebrandt,et al.  Constructive proofs of representation theorems in separable Hilbert space , 1964 .

[16]  Milo R. Dorr,et al.  The Approximation Theory for the p-Version of the Finite Element Method , 1984 .

[17]  Ivo Babuška,et al.  The optimal convergence rate of the p-version of the finite element method , 1987 .

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

[19]  I. Babuska,et al.  The h , p and h-p versions of the finite element methods in 1 dimension . Part III. The adaptive h-p version. , 1986 .

[20]  I Babuska,et al.  The p and h-p Versions of the Finite Element Method; State of the Art. , 1986 .

[21]  I. Babuska,et al.  Theh,p andh-p versions of the finite element method in 1 dimension , 1986 .

[22]  Wolfgang L. Wendland,et al.  ON SOME MATHEMATICAL ASPECTS OF BOUNDARY ELEMENT METHODS FOR ELLIPTIC PROBLEMS , 1985 .

[23]  Ivo Babuška,et al.  The h-p version of the finite element method , 1986 .

[24]  E. Alarcon,et al.  p-adaptive boundary elements , 1986 .