Kopriva-benchmark

Toy project for DG method.

Timeline

• Quadrature nodes and weights
• Nodal representation
  • Lagrange interpolation
  • Differentiation matrix
• DG approximation
• Time evolution
• Splitting domain
• Flux
• ...
• Completed!

Benchmark for $N=6$ Gauss points (Kopriva p.67 Table 3.1)

• Gauss

$j$	$x_j$	$w_j$
0	-0.949107912342758	0.129484966168870
1	-0.741531185599394	0.279705391489277
2	-0.405845151377397	0.381830050505119
3	0.000000000000000	0.417959183673469

• Gauss-Lobatto

$j$	$x_j$	$w_j$
0	-1.000000000000000	0.047619047619048
1	-0.830223896278567	0.276826047361566
2	-0.468848793470714	0.431745381209863
3	0.000000000000000	0.487619047619048