using the l2-norm, estimate the error on the pressure gradient ranging from – 4 to 0.4 with a spatial resolution of 0.2. in matlab

Assuming that the pressure gradient is represented by a function f(x) and that its true or exact value is unknown, the error of an approximate solution g(x) can be estimated using the L2-norm as follows:

main.m
x = -4:0.2:0.4;  % spatial locations
f = ...  % true pressure gradient function
g = ...  % approximate pressure gradient function

error = sqrt(sum((f-g).^2.*(0.2)^2));  % L2-norm error estimate
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Here, f-g represents the difference between the true and approximate solutions at each location, (0.2)^2 represents the square of the spatial resolution, and the sum and sqrt functions perform the summation and square root required by the L2-norm formula.

Note that the choice of the approximate solution g and the spatial resolution 0.2 will affect the accuracy of the error estimate. In general, higher-resolution approximations should provide more accurate error estimates. Additionally, if the true solution f is not known, it may be difficult to judge the accuracy of the error estimate.