AbstractA new higher-order accurate space-time discontinuous Galerkin (DG) method using the interior penalty flux and discontinuous basis functions, both in space and in time, is presented and fully analyzed for the second-order scalar wave equation. Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method. The theoretical analysis shows that the DG discretization is stable and converges in a DG-norm on general unstructured and locally refined meshes, including local refinement in time. The space-time interior penalty DG discretization does not have a CFL-type restriction for stability. Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time step $$\Delta t$$
Δ
t
satisfy $$h\cong C\Delta t$$
h
≅
C
Δ
t
, with C a positive constant. The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems. These calculations also show that for pth-order tensor product basis functions the convergence rate in the $$L^\infty$$
L
∞
and $$L^2$$
L
2
-norms is order $$p+1$$
p
+
1
for polynomial orders $$p=1$$
p
=
1
and $$p=3$$
p
=
3
and order p for polynomial order $$p=2$$
p
=
2
.