Discontinuous Galerkin Methods For Weakly Coupled Hyperbolic Multi-domain Problems

In this thesis,we develop and analyze the Runge-Kutta discontinuous Galerkin(RKDG)method to solve weakly coupled hyperbolic multi-domain problems.Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains,calling for special techniques to prove well-posedness of model prob-lems and efficiency of the RKDG methods.We prove both stability and error estimates for our RKDG methods on simple models,and then apply them to a biological cell proliferation model.According to the nonnegative property of cell density in biolog-ical cell proliferation model,we apply the bounded-preserving limiter and obtain the positivity-preserving DG scheme.Numerical results are provided to illustrate the good behavior of our RKDG methods.