A DPG-based time-marching scheme for linear hyperbolic problems

The Discontinuous Petrov–Galerkin (DPG) method is a widely employed discretization for Partial Differential Equations (PDEs). In recent work, we applied the DPG with optimal test functions time integration of transient parabolic PDEs. We showed that resulting DPG-based time-marching scheme equivalent to exponential integrators trace variables. this extend aforementioned time-dependent hyperbolic For that, reduce second order system in first and calculate testing analytically. also relate our Gautschi-type. Finally, validate 1D/2D + linear wave equation after semidiscretization space standard Bubnov–Galerkin method. presented integrator provides expressions solution element interiors addition those on traces. This allows design different error estimators perform adaptivity.