# Error analysis of the quartic nodal expansion method for slab geometry

## Abstract

This paper presents an analysis of the quartic polynomial Nodal Expansion Method (NEM) for one-dimensional neutron diffusion calculations. As part of an ongoing effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal kinetics codes, we derive a priori error bounds on the computed solution for uniform meshes and validate them using a simple test problem. Predicted error bounds are found to be greater than computed maximum absolute errors by no more than a factor of six allowing mesh size selection to reflect desired accuracy. We also quantify the rapid convergence in the NEM computed solution as a function of mesh size.

- Authors:

- North Carolina State Univ., Raleigh, NC (United States)
- Oak Ridge National Lab., TN (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10122628

- Report Number(s):
- CONF-950420-19

ON: DE95007373; TRN: 95:002593

- DOE Contract Number:
- AC05-84OR21400

- Resource Type:
- Conference

- Resource Relation:
- Conference: International conference on mathematics and computations, reactor physics, and environmental analyses,Portland, OR (United States),30 Apr - 4 May 1995; Other Information: PBD: [1995]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NUMERICAL SOLUTION; ACCURACY; NEUTRON DIFFUSION EQUATION; NEUTRON TRANSPORT; COMPUTERIZED SIMULATION; N CODES; 663610; 220100; 990200; NEUTRON PHYSICS; THEORY AND CALCULATION; MATHEMATICS AND COMPUTERS

### Citation Formats

```
Penland, R.C., Turinsky, P.J., and Azmy, Y.Y.
```*Error analysis of the quartic nodal expansion method for slab geometry*. United States: N. p., 1995.
Web.

```
Penland, R.C., Turinsky, P.J., & Azmy, Y.Y.
```*Error analysis of the quartic nodal expansion method for slab geometry*. United States.

```
Penland, R.C., Turinsky, P.J., and Azmy, Y.Y. Wed .
"Error analysis of the quartic nodal expansion method for slab geometry". United States. https://www.osti.gov/servlets/purl/10122628.
```

```
@article{osti_10122628,
```

title = {Error analysis of the quartic nodal expansion method for slab geometry},

author = {Penland, R.C. and Turinsky, P.J. and Azmy, Y.Y.},

abstractNote = {This paper presents an analysis of the quartic polynomial Nodal Expansion Method (NEM) for one-dimensional neutron diffusion calculations. As part of an ongoing effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal kinetics codes, we derive a priori error bounds on the computed solution for uniform meshes and validate them using a simple test problem. Predicted error bounds are found to be greater than computed maximum absolute errors by no more than a factor of six allowing mesh size selection to reflect desired accuracy. We also quantify the rapid convergence in the NEM computed solution as a function of mesh size.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1995},

month = {2}

}

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