Volume 7, Issue 3
Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations

Hongling Hu & Chuanmiao Chen

Adv. Appl. Math. Mech., 7 (2015), pp. 323-337.

Published online: 2018-05

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  • Abstract

In this paper, we present a superconvergence result for the bi-$k$ degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is one order higher than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.

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@Article{AAMM-7-323, author = {}, title = {Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {3}, pages = {323--337}, abstract = {

In this paper, we present a superconvergence result for the bi-$k$ degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is one order higher than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m615}, url = {http://global-sci.org/intro/article_detail/aamm/12050.html} }
TY - JOUR T1 - Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 323 EP - 337 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2014.m615 UR - https://global-sci.org/intro/article_detail/aamm/12050.html KW - AB -

In this paper, we present a superconvergence result for the bi-$k$ degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is one order higher than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.

Hongling Hu & Chuanmiao Chen. (1970). Superconvergence of bi-$k$ Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations. Advances in Applied Mathematics and Mechanics. 7 (3). 323-337. doi:10.4208/aamm.2014.m615
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