Main

Define Filter

Select Notation

Conventions

Reference Solutions

Similar Web Sites

About cookies

Conventions, Notations and Terminology

For many problems with a known exact solution, the right hand side of the differential equation is given as f (or f1 or some other related form) and the right hand side of the boundary condition is given as g (or a related form). In this case the right hand side is determined by applying the operator to the exact solution.

Poisson's Equation (in 2D) is -uxx - uyy = f, with the obvious modifications for other numbers of dimensions.

Laplace's Equation is Poisson's Equations with f = 0.

The Dirichlet boundary condition is u = g.

The Neumann boundary condition is ∂u/∂n = g where n is the outward unit normal.

The natural boundary condition for (for example) -∇·(pu)=f is pu·n=g where n is the outward unit normal vector.
When p=1, the natural boundary conditions are Neumann.

The unit interval is (0,1).
The unit square is (0,1)X(0,1).
The unit cube is (0,1)X(0,1)X(0,1).




The National Institute of Standards and Technology (NIST) is an agency of the U.S. Department of Commerce.

Privacy Policy / Security Notice / Accessibility Statement / Disclaimer / Freedom of Information Act (FOIA) /
Environmental Policy Statement / No Fear Act Policy / NIST Information Quality Standards /
Scientific Integrity Summary

Date created: May 16, 2013 | Last updated: March 16, 2018    Contact: William Mitchell, Home Page
Development status: Active maintenance