# A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

## Abstract

We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.

- Authors:

- University of Novi Sad, Department of Mathematics and Informatics, Faculty of Sciences (Serbia)
- Technical University of Dresden, Institute of Numerical Mathematics (Germany)
- University of Novi Sad, Department for Fundamental Disciplines, Faculty of Technical Sciences (Serbia)

- Publication Date:

- OSTI Identifier:
- 22769389

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY-VALUE PROBLEMS; CONVERGENCE; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; POLYNOMIALS

### Citation Formats

```
Zarin, Helena, Roos, Hans-Görg, and Teofanov, Ljiljana.
```*A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0339-3.

```
Zarin, Helena, Roos, Hans-Görg, & Teofanov, Ljiljana.
```*A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem*. United States. doi:10.1007/S40314-016-0339-3.

```
Zarin, Helena, Roos, Hans-Görg, and Teofanov, Ljiljana. Thu .
"A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem". United States. doi:10.1007/S40314-016-0339-3.
```

```
@article{osti_22769389,
```

title = {A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem},

author = {Zarin, Helena and Roos, Hans-Görg and Teofanov, Ljiljana},

abstractNote = {We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.},

doi = {10.1007/S40314-016-0339-3},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}

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