README.md

Intro

A CPP code developed to solve 1D pure-diffusion problem in FEM using continuous Galerkin method.

Phsical problem

$$u_{,xx} + f(x) = 0 \quad \Sigma = (0,L)$$

$$u(0) = u_{exact}(0)$$

$$u_{,x}(L) = u_{exact,x}(L)$$

Exact solution

$$u_{exact} = sin(x)$$

Code details

void Gauss(int N, double a, double * qp, double * wq) assigns values to qp and wq.

double Polybasis(const int &degree, int i, int der, double &x) returns specific value of Lagrange-shape function.

double Func_source(const double &x) returns value of $f(x)$.

double Func_exact(const double &x) returns value of exact solution but not used.

double Func_exact_x(const double &x) returns value of 1st derivative of exact solution but not used.

Run the code

1. Run mkdir build under FEM-1D_CG_CPP/ to create a new directory.
2. Run cd build to step in the new directory.
3. Run cmake .. to create makefile using CMakeLists.txt from upper directory.
4. Run make to create an executable file named 1D_CG_CPP.
5. Run ./1D_CG_CPP.