Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation

2014 ◽  
Vol 31 (5) ◽  
pp. 1461-1491 ◽  
Author(s):  
Mahboub Baccouch
Keyword(s):  
Wave Equation ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Second Order ◽  
A Posteriori ◽  
One Dimensional ◽  
Local Discontinuous Galerkin ◽  
Second Order Wave Equation ◽  
The One

On the error estimates of a hybridizable discontinuous Galerkin method for second-order elliptic problem with discontinuous coefficients

2019 ◽  
Vol 40 (2) ◽  
pp. 1577-1600
Author(s):  
Gang Chen ◽  
Jintao Cui
Keyword(s):  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Elliptic Problem ◽  
Posteriori Error ◽  
Discontinuous Coefficients ◽  
Second Order ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Hybridizable Discontinuous Galerkin ◽  
Order Elliptic Problem

Abstract Hybridizable discontinuous Galerkin (HDG) methods retain the main advantages of standard discontinuous Galerkin (DG) methods, including their flexibility in meshing, ease of design and implementation, ease of use within an $hp$-adaptive strategy and preservation of local conservation of physical quantities. Moreover, HDG methods can significantly reduce the number of degrees of freedom, resulting in a substantial reduction of computational cost. In this paper, we study an HDG method for the second-order elliptic problem with discontinuous coefficients. The numerical scheme is proposed on general polygonal and polyhedral meshes with specially designed stabilization parameters. Robust a priori and a posteriori error estimates are derived without a full elliptic regularity assumption. The proposed a posteriori error estimators are proved to be efficient and reliable without a quasi-monotonicity assumption on the diffusion coefficient.

CTCS Schemes for Second Order Wave Equation: Numerical Results and Spectral Analysis

2021 ◽  
Vol 55 ◽  
pp. 47-65
Author(s):  
Appanah Rao Appadu ◽  
Gysbert Nicolaas de Waal
Keyword(s):  
Spectral Analysis ◽  
Wave Equation ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Second Order ◽  
Numerical Results ◽  
Order Accuracy ◽  
Constant Coefficients ◽  
Second Order Wave Equation ◽  
The One

IIn this paper, two finite difference methods are used to solve the one-dimensional second order wave equation with constant coefficients subject to specified initial and boundary conditions. Two numerical experiments are considered. The two methods are Central in Time and Central in Space scheme with second order accuracy in both time and space, abbreviated as CTCS (2,2) and Central in Time and Central in Space scheme with second order accuracy in time and fourth order accuracy in space, abbreviated as CTCS (2,4). Properties such as consistency and stability are studied. We also perform spectral analysis of dispersive and dissipative properties of the two methods. Two numerical experiments are considered, and the numerical results are displayed.

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