### 4.7 Kernel

This directory contains two files, kernel.h and kernel.cpp, both of which are related to the
line-SIAC (L-SIAC) filtering [27, 43] of FEM solutions. SIAC filtering takes the
form:

where u_{h} denotes the FEM (continuous Galkerkin or discontinuous Galerkin) solution and K_{H}
represents a kernel function:

In this expression, the functions ψ(x) are B-Splines. The two kernel files in this directory
provide all the tools needed to construct the B-Spline functions and the kernel function
described above.