# A simple finite element method for linear hyperbolic problems

## Abstract

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
- Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)

- OSTI Identifier:
- 1407723

- Alternate Identifier(s):
- OSTI ID: 1495741

- Grant/Contract Number:
- [AC05-00OR22725; DMS-1620016; ERKJE45]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational and Applied Mathematics

- Additional Journal Information:
- [ Journal Volume: 330; Journal Issue: C]; Journal ID: ISSN 0377-0427

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Finite element methods; Hyperbolic equations

### Citation Formats

```
Mu, Lin, and Ye, Xiu. A simple finite element method for linear hyperbolic problems. United States: N. p., 2017.
Web. doi:10.1016/j.cam.2017.08.025.
```

```
Mu, Lin, & Ye, Xiu. A simple finite element method for linear hyperbolic problems. United States. doi:10.1016/j.cam.2017.08.025.
```

```
Mu, Lin, and Ye, Xiu. Thu .
"A simple finite element method for linear hyperbolic problems". United States. doi:10.1016/j.cam.2017.08.025. https://www.osti.gov/servlets/purl/1407723.
```

```
@article{osti_1407723,
```

title = {A simple finite element method for linear hyperbolic problems},

author = {Mu, Lin and Ye, Xiu},

abstractNote = {Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.},

doi = {10.1016/j.cam.2017.08.025},

journal = {Journal of Computational and Applied Mathematics},

number = [C],

volume = [330],

place = {United States},

year = {2017},

month = {9}

}

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