A Space-Time Interior Penalty Discontinuous Galerkin Method for the Wave Equation  

作　　者：Poorvi Shukla J.J.W.van der Vegt 

机构地区：[1]Department of Applied Mathematics,University of Twente,P.O.Box 217,7500 AE Enschede,The Netherlands

出　　处：《Communications on Applied Mathematics and Computation》2022年第3期904-944,共41页应用数学与计算数学学报（英文）

摘　　要：A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.

关 键 词：Wave equation Space-time methods Discontinuous Galerkin methods Interior penalty method A priori error analysis 

分 类 号：O17[理学—数学]