Description
Return one linear finite-element shape function and derivative.
Numerical grids and sampled modes require explicit coordinate, boundary and sign conventions. A staggered location, minimum-image gap or Nyquist label is one component of a discretization rather than a complete field solve or unique physical interpretation.
Return one linear finite-element shape function and derivative.
When to use this tool
Use Finite Element Linear Shape One Node when checking the stated grid-coordinate, periodic-image or sampled-mode convention.
How to use the tool and how it works
- Enter coordinate, left, right, node. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shape, derivative. Use the output convention below.
Return one linear finite-element shape function and derivative. Require right > left, coordinate inside the closed segment and node left or right; shape is the corresponding linear endpoint weight, derivative is minus/plus 1/(right-left).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| node | Node | Required. Text; one of "left", "right"; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shape | Shape | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
{
"input": {
"coordinate": 1,
"left": 0,
"right": 4,
"node": "left"
},
"output": {
"shape": 0.75,
"derivative": -0.25
}
}Limitations and assumptions
- The derivative uses inverse-coordinate units; this is one local element term rather than assembly, integration or a solved field.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete mesh, transform convention and boundary conditions for a consistent numerical simulation or physical interpretation.
References
Similar or alternative tools
- Numerical Dispersion One Grid Phase
Compare a centered spatial derivative's mode factor with exact wavenumber.
- Poisson Stencil One Source Term
Scale one Poisson-stencil source contribution.