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Volume 29, Issue 5
A Numerical Boundary Eigenvalue Problem for Elastic Cracks in Free and Half Space

Darko Volkov

DOI: 10.4208/jcm.1106-m3406

J. Comp. Math., 29 (2011), pp. 543-573.

Published online: 2011-10

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  • Abstract

We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems: additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered: the Laplace equation in free space, the linear elasticity equation in free space, and in half space.

  • Keywords

Hypersingular boundary integral equations, Numerical error analysis, Eigenvalue problems, Faults in free space and half space, Somigliana tensor of the second kind in free space and in half space.

  • AMS Subject Headings

45L05, 65R20, 86-08.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-543, author = {Darko Volkov}, title = {A Numerical Boundary Eigenvalue Problem for Elastic Cracks in Free and Half Space}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {5}, pages = {543--573}, abstract = {

We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems: additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered: the Laplace equation in free space, the linear elasticity equation in free space, and in half space.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1106-m3406}, url = {http://global-sci.org/intro/article_detail/jcm/8492.html} }
TY - JOUR T1 - A Numerical Boundary Eigenvalue Problem for Elastic Cracks in Free and Half Space AU - Darko Volkov JO - Journal of Computational Mathematics VL - 5 SP - 543 EP - 573 PY - 2011 DA - 2011/10 SN - 29 DO - http://doi.org/10.4208/jcm.1106-m3406 UR - https://global-sci.org/intro/article_detail/jcm/8492.html KW - Hypersingular boundary integral equations, Numerical error analysis, Eigenvalue problems, Faults in free space and half space, Somigliana tensor of the second kind in free space and in half space. AB -

We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems: additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered: the Laplace equation in free space, the linear elasticity equation in free space, and in half space.

Darko Volkov. (2011). A Numerical Boundary Eigenvalue Problem for Elastic Cracks in Free and Half Space. Journal of Computational Mathematics. 29 (5). 543-573. doi:10.4208/jcm.1106-m3406
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