Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations

被引:13
|
作者
Schutz, Jochen [1 ]
Seal, David C. [2 ]
Jaust, Alexander [1 ]
机构
[1] Hasselt Univ, Computat Math Grp, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium
[2] US Naval Acad, Dept Math, 572C Holloway Rd, Annapolis, MD 21402 USA
关键词
Discontinuous Galerkin; Convection-diffusion; Implicit multiderivative; Lax-Wendroff; Collocation methods; RUNGE-KUTTA METHODS; ESSENTIALLY NONOSCILLATORY SCHEMES; HERMITE-BIRKHOFF-INTERPOLATION; HYPERBOLIC CONSERVATION-LAWS; TIME DISCRETIZATIONS; HIGHER DERIVATIVES; FORMULATION; SYSTEMS; EULER; ODES;
D O I
10.1007/s10915-017-0485-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax-Wendroff (Taylor) as well as Runge-Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.
引用
收藏
页码:1145 / 1163
页数:19
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