2015/10/27 by Alexander Jaust, Jaust, Alexander, Jochen Schütz +3 · 1 citation
Mathematics · Earth and Planetary Sciences · #Numerical methods for differential equations #Fractional Differential Equations Solutions #Meteorological Phenomena and Simulations
paper · pdf · doi:10.48550/arxiv.1510.08181
In this paper we apply implicit two-derivative multistage time integrators to\nviscous conservation laws in one and two dimensions. The one dimensional solver\ndiscretizes space with the classical discontinuous Galerkin (DG) method, and\nthe two dimensional solver uses a hybridized discontinuous Galerkin (HDG)\nspatial discretization for efficiency. We propose methods that permit us to\nconstruct implicit solvers using each of these spatial discretizations, wherein\na chief difficulty is how to handle the higher derivatives in time. The end\nresult is that the multiderivative time integrator allows us to obtain\nhigh-order accuracy in time while keeping the number of implicit stages at a\nminimum. We show numerical results validating and comparing methods.\n