# Application of Mass Lumped Higher Order Finite Elements

## Abstract

There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.

- Authors:

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 934516

- Report Number(s):
- PPPL-4128

TRN: US0804644

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCURACY; STELLARATORS; TRANSPORT; Higher order finite elements; mass lumping; highly anisotropic transport

### Citation Formats

```
Chen, J., Strauss, H. R., Jardin, S. C., Park, W., Sugiyama, L. E., G. Fu, and Breslau, J.
```*Application of Mass Lumped Higher Order Finite Elements*. United States: N. p., 2005.
Web. doi:10.2172/934516.

```
Chen, J., Strauss, H. R., Jardin, S. C., Park, W., Sugiyama, L. E., G. Fu, & Breslau, J.
```*Application of Mass Lumped Higher Order Finite Elements*. United States. doi:10.2172/934516.

```
Chen, J., Strauss, H. R., Jardin, S. C., Park, W., Sugiyama, L. E., G. Fu, and Breslau, J. Tue .
"Application of Mass Lumped Higher Order Finite Elements". United States.
doi:10.2172/934516. https://www.osti.gov/servlets/purl/934516.
```

```
@article{osti_934516,
```

title = {Application of Mass Lumped Higher Order Finite Elements},

author = {Chen, J. and Strauss, H. R. and Jardin, S. C. and Park, W. and Sugiyama, L. E. and G. Fu and Breslau, J.},

abstractNote = {There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.},

doi = {10.2172/934516},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}