Page 378 - Process Modelling and Simulation With Finite Element Methods

A MATLAB/FEMLAB Primer for Vector Calculus 365

FEMLAB provides a special post interp function to extract interpolated
values from fem.sol for each dependent variable and derived variable. The book
is littered with examples of using postinterp to represent functions. It can even
be automated in an m-file function that calls the appropriate fem structure from a
mat-file.

A.4 Differentiation in Multivariable Calculus

A.4.1 The gradient of a scalar field
If $=$(x,y,z), then the vector

is called the gradient of the scalar field $, and is denoted as well by grad $. The
gradient operator v (the nabla character) is the vector operator
a .a a
V=i-+j--+k-
ax ay az

in Cartesian coordinates in 3-D.

A FEMLAB example. Suppose 4 = x2 + y2, then V$ = (2x, 2y, 0).

But MATLAB does not directly deal with such symbolic calculations, however
its symbolic toolbox does. FEMLAB, however, routinely calculates the
numerical approximation of the derivatives of a solution. So the gradient of a
scalar field can be constructed by FEMLAB “primitive” operations. How do we
easily access this information? Here’s the recipe.