Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: hp version

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2020.01.017 ◽

2020 ◽

Vol 79 (11) ◽

pp. 3223-3240 ◽

Author(s):

Yu Du ◽

Jiangxing Wang

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Convergence Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Second Order ◽

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Convergence Analysis of a Discontinuous Galerkin Method for Wave Equations in Second-Order Form

SIAM Journal on Numerical Analysis ◽

10.1137/18m1190495 ◽

2019 ◽

Vol 57 (1) ◽

pp. 238-265 ◽

Author(s):

Yu Du ◽

Lu Zhang ◽

Zhimin Zhang

Keyword(s):

Galerkin Method ◽

Convergence Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Wave Equations ◽

Second Order ◽

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A high-order space–time ultra-weak discontinuous Galerkin method for the second-order wave equation in one space dimension

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113331 ◽

2021 ◽

Vol 389 ◽

pp. 113331

Author(s):

Mahboub Baccouch ◽

Helmi Temimi

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Space Dimension ◽

Second Order ◽

Second Order Wave Equation ◽

One Space Dimension

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An Adaptive Multiresolution Interior Penalty Discontinuous Galerkin Method for Wave Equations in Second Order Form

Journal of Scientific Computing ◽

10.1007/s10915-020-01322-w ◽

2020 ◽

Vol 85 (1) ◽

Author(s):

Juntao Huang ◽

Yuan Liu ◽

Wei Guo ◽

Zhanjing Tao ◽

Yingda Cheng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Wave Equations ◽

Second Order ◽

Interior Penalty ◽

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A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation

SIAM Journal on Numerical Analysis ◽

10.1137/16m1065744 ◽

2017 ◽

Vol 55 (1) ◽

pp. 63-86 ◽

Author(s):

Lehel Banjai ◽

Emmanuil H. Georgoulis ◽

Oluwaseun Lijoka

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Second Order ◽

Polynomial Space ◽

Second Order Wave Equation

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A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.08.023 ◽

2014 ◽

Vol 68 (10) ◽

pp. 1250-1278 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation

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An energy‐based discontinuous Galerkin method for coupled elasto‐acoustic wave equations in second‐order form

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6065 ◽

2019 ◽

Vol 119 (7) ◽

pp. 618-638 ◽

Author(s):

Daniel Appelö ◽

Siyang Wang

Keyword(s):

Acoustic Wave ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Wave Equations ◽

Second Order ◽

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A local discontinuous Galerkin method for the second-order wave equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2011.10.012 ◽

2012 ◽

Vol 209-212 ◽

pp. 129-143 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation

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Superconvergence of the local discontinuous galerkin method applied to the one-dimensional second-order wave equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21840 ◽

2013 ◽

Vol 30 (3) ◽

pp. 862-901 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation ◽

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7077 ◽

2020 ◽

Author(s):

Hadi Mohammadi‐Firouzjaei ◽

Hojatollah Adibi ◽

Mehdi Dehghan

Keyword(s):

Wave Equation ◽

Laplace Transform ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Wave ◽

Local Discontinuous Galerkin ◽

Distributed Order

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