TY - JOUR
T1 - Computing singular solutions of elliptic boundary value problems in polyhedral domains using the p-FEM
AU - Yosibash, Zohar
N1 - Funding Information:
The author would like to thank Profs. Martin Costabel and Monique Dauge of University of Rennes 1, France, for their valuable comments on the space of admissible fluxes. The reported work has been partially supported by the AFOSR under STTR/TS project No. F-49620-97-C-0045.
PY - 2000/1/1
Y1 - 2000/1/1
N2 - Numerical methods for computing singular solutions of linear second order elliptic partial differential equations (Laplace and Elasticity problems) in polyhedral domains are presented. The singularities may be caused by edges, vertices, or abrupt changes in material properties or boundary conditions. In the vicinity of the singular lines or points the solution can be represented by an asymptotic series, composed of eigen-pairs and their amplitudes. These are of great interest from the point of view of failure initiation because failure theories directly or indirectly involve them. This paper addresses a general method based on the modified Steklov formulation for computing the eigen-pairs and a dual weak formulation for extracting the amplitudes numerically using the p-version of the finite element method. The methods are post-solution operations on the finite element solution vector and have been shown in a two dimensional setting to be super-convergent.
AB - Numerical methods for computing singular solutions of linear second order elliptic partial differential equations (Laplace and Elasticity problems) in polyhedral domains are presented. The singularities may be caused by edges, vertices, or abrupt changes in material properties or boundary conditions. In the vicinity of the singular lines or points the solution can be represented by an asymptotic series, composed of eigen-pairs and their amplitudes. These are of great interest from the point of view of failure initiation because failure theories directly or indirectly involve them. This paper addresses a general method based on the modified Steklov formulation for computing the eigen-pairs and a dual weak formulation for extracting the amplitudes numerically using the p-version of the finite element method. The methods are post-solution operations on the finite element solution vector and have been shown in a two dimensional setting to be super-convergent.
UR - http://www.scopus.com/inward/record.url?scp=0034190276&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(99)00071-9
DO - 10.1016/S0168-9274(99)00071-9
M3 - Conference article
AN - SCOPUS:0034190276
SN - 0168-9274
VL - 33
SP - 71
EP - 93
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 1
T2 - The 4th International Conference on Spectral and High Order Methods (ICOSAHOM 1998)
Y2 - 22 June 1998 through 26 June 1998
ER -