Efficient numerical realization of discontinuous Galerkin methods for temporal discretization of parabolic problems
The authors propose an efficient numerical realization of discontinuous Galerkin methods (dG) for temporal discretization of parabolic partial differential equations of the form \(\partial_t u(t) + A(u) = f(t)\),\; \(t \in (0,T)\), with initial condition \(u(0) = u_0\). Two sets of assumptions are imposed on the spatial differential operator that guarantee the existence of a unique solution and the applicability of the proposed simplified solution scheme. A suitable approximation to Newton's method and decoupling the Newton update equation, which consists of a coupled system of \(r+1\) elliptic problems will avoid complex coefficients which arise inevitably in the equations obtained by a direct decoupling. The accuracy of these approximations and their impact on the outer Newton iteration are investigated. The efficiency of the presented schemes is studied by numerical tests.
scientific article; zbMATH DE number 6162441
scientific article