# The numerical methods for oscillating singularities in elliptic boundary value problems

@article{Oh2001TheNM, title={The numerical methods for oscillating singularities in elliptic boundary value problems}, author={Hae-Soo Oh and Hoonjoo Kim and Sungjin Lee}, journal={Journal of Computational Physics}, year={2001}, volume={170}, pages={742-763} }

The singularities near the crack tips of homogeneous materials are monotone of type rα and rα logδr (depending on the boundary conditions along nonsmooth domains). However, the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type rα sin(e log r). The method of auxiliary mapping (MAM), introduced by Babuska and Oh, was proven to be successful in dealing with rα type singularities. However, the effectiveness of MAM is reduced in handling oscillating…

## 15 Citations

### Numerical methods and error analysis for one dimensional elliptic problems containing singularities

- Mathematics
- 2003

The method of auxiliary mapping (MAM), introduced by Babuška and Oh, was proven to be very successful in dealing with monotone singularities arising in two‐dimensional problems. In this article, in…

### Numerical Methods for Accurate Finite Element Solutions of Elliptic Boundary Value Problems Containing Singularities

- Mathematics
- 2002

The Method of Auxiliary Mapping (MAM), introduced by Babuska and Oh, was proven to be very successful in dealing with monotone singularities arising in two dimensional problems. In this paper, in the…

### Mapping Techniques for Isogeometric Analysis of Elliptic Boundary Value Problems Containing Singularities

- Mathematics
- 2013

### Reproducing Polynomial ( Singularity ) Particle Methods and Adaptive Meshless Methods for 2-Dim Elliptic Boundary Value Problems by

- Mathematics, Computer Science
- 2008

This paper introduces RPPM (Reproducing Polynomial Particle Methods) that is the Galerkin approximation method associated with the use of the RPP approximation space and introduces adaptive patchwise RPPM and compares it with RSPM.

### Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners

- Mathematics
- 2014

The mapping method was introduced in Jeong et al. (2013) for highly accurate isogeometric analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned…

### Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

- Mathematics
- 2016

We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary…

### The p-version of the FEM for slowly oscillating singularities in one dimension

- Mathematics

We analyse the p-version of the finite element method on an interval for the approximation of slowly oscillating singularities. We prove an asymptotically exact a priori error estimate by studying…

### Reproducing polynomial (singularity) particle methods and adaptive meshless methods for two-dimensional elliptic boundary value problems

- Computer Science, Mathematics
- 2009

### The reproducing singularity particle shape functions for problems containing singularities

- Mathematics
- 2007

In this paper, we construct particle shape functions that reproduce singular functions as well as polynomial functions. We also construct piecewise polynomial convolution partition of unity functions…

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