Singular Isoparametric Finite Elements

Wait, R.

doi:10.1093/imamat/20.1.133

Cited by 26 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus other finite element techniques for dealing with three-dimensional singularities must be mentioned, although the above error analysis is not immediately applicable to them. Such methods include three-dimensional versions of the so called '$-point' elements of Henshell and Shaw,12 such as that due to Wait,22 where special cubic elements with distortions of certain nodes are made to produce an approximation to the p2/3 singular behaviour. An alternative is the approach of Akin,' who uses special basis functions appropriate to the line singularity.…”

Section: Practical Implicationsmentioning

confidence: 99%

Singularities of the Laplacian at corners and edges of three‐dimensional domains and their treatment with finite element methods

Stephan

Whiteman

1988

Math Methods in App Sciences

View full text Add to dashboard Cite

Communicated by W. WendlandThree-dimensional Poisson problems containing boundary singularities are treated. The forms of the solutions for certain problems of this type are derived, where the domains of the problems can be represented in terms either of spherical-or of cylindrical-polar co-ordinates. These singular forms are used to augment the basis of a standard piecewise polynomial Galerkin space, thus producing an augmented Galerkin technique which is suited to the context of a problem involving a singularity. Error estimates are derived.

show abstract

Section: Practical Implicationsmentioning

confidence: 99%

Singularities of the Laplacian at corners and edges of three‐dimensional domains and their treatment with finite element methods

Stephan

Whiteman

1988

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…There exist results concerning isoparametric elements with singularities in the context of finite element methods. In [20,21] singular isoparametric finite elements are used to approximate singularities in the solution. The results for such finite elements could be generalized to B-spline parameterizations, but the problems and results presented there differ from the problems considered in this paper.…”

Section: Introductionmentioning

confidence: 99%