Space-time residual distribution schemes for hyperbolic conservation laws on unstructured linear finite elements

2002 ◽  
Vol 40 (3-4) ◽  
pp. 573-581 ◽  
Author(s):  
Á. Csík ◽  
H. Deconinck
Keyword(s):  
Finite Elements ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Space Time ◽  
Residual Distribution ◽  
Hyperbolic Conservation ◽  
Residual Distribution Schemes

A Compact High Order Space-Time Method for Conservation Laws

2011 ◽  
Vol 9 (2) ◽  
pp. 441-480 ◽  
Author(s):  
Shuangzhang Tu ◽  
Gordon W. Skelton ◽  
Qing Pang
Keyword(s):  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Space Time ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Time Step ◽  
Order Of Accuracy ◽  
Hyperbolic Conservation

AbstractThis paper presents a novel high-order space-time method for hyperbolic conservation laws. Two important concepts, the staggered space-time mesh of the space-time conservation element/solution element (CE/SE) method and the local discontinuous basis functions of the space-time discontinuous Galerkin (DG) finite element method, are the two key ingredients of the new scheme. The staggered space-time mesh is constructed using the cell-vertex structure of the underlying spatial mesh. The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes. The solution within each physical time step is updated alternately at the cell level and the vertex level. For this solution updating strategy and the DG ingredient, the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme (DG-CVS). The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE. The present DG-CVS exhibits many advantageous features such as Riemann-solver-free, high-order accuracy, point-implicitness, compactness, and ease of handling boundary conditions. Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.

scholarly journals Entropy Stable Space–Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws

2019 ◽  
Vol 80 (1) ◽  
pp. 175-222 ◽  
Author(s):  
Lucas Friedrich ◽  
Gero Schnücke ◽  
Andrew R. Winters ◽  
David C. Del Rey Fernández ◽  
Gregor J. Gassner ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Space Time ◽  
Summation By Parts ◽  
Hyperbolic Conservation ◽  
Stable Space ◽  
Entropy Stable
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