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Jul 12, 2021
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Fix small grammar mistakes #39

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6 changes: 3 additions & 3 deletions chapter1/fundamentals_code.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -46,7 +46,7 @@
"\n",
"Note that in many cases, it can be hard to determine if the program works if it produces an error of size $10^{-5}$ on a\n",
"$20 \\times 20$ grid. However, since we are using Sobolev spaces,\n",
"we usually known about the numerical errors _asymptotic properties_. For instance that it is proportional to $h^2$ if $h$ is the size of a cell in the mesh. We can then compare the error on meshes with different $h$-values to see if the asymptotic behavior is correct. This technique will be explained in detail in the chapter [Improving your fenics code](./../chapter4/convergence).\n",
"we usually know about the numerical errors _asymptotic properties_. For instance that it is proportional to $h^2$ if $h$ is the size of a cell in the mesh. We can then compare the error on meshes with different $h$-values to see if the asymptotic behavior is correct. This technique will be explained in detail in the chapter [Improving your fenics code](./../chapter4/convergence).\n",
"\n",
"However, in cases where we have a solution we know that should have no approximation error, we know that the solution should\n",
"be produced to machine precision by the program.\n",
Expand Down Expand Up @@ -91,7 +91,7 @@
"which defines a uniform finite element mesh over the unit square $[0,1]\\times[0, 1]$. The mesh consists of _cells_, which in 2D can be either triangles of quadrilaterals. Note that in addition to give how many elements we would like to have in each direction. \n",
"Note that we also supply the _MPI-communicator_. \n",
"This is to specify how we would like the program to behave in parallel. If we supply `MPI.COMM_WORLD` we create a single mesh,\n",
"which data is distributed over the number of processors we \n",
"whose data is distributed over the number of processors we \n",
"would like to use. We can for instance run the program in \n",
"parallel on two processors by using `mpirun`, as: \n",
"``` bash\n",
Expand Down Expand Up @@ -534,4 +534,4 @@
},
"nbformat": 4,
"nbformat_minor": 4
}
}