Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios. --
%0 Book
%1 cangiani2017hpversion
%A Cangiani, Andrea
%A Dong, Zhaonan
%A Georgoulis, Emmanuil H.
%A Houston, Paul
%B Springer Briefs in Mathematics
%C Cham
%D 2017
%I Springer
%K 35j25-bvps-2nd-order-elliptic-equations 35l02-first-order-hyperbolic-equations 35m12-pdes-bvps-mixed-type 65-02-numerical-analysis-research-exposition 65m08-pdes-ibvps-finite-volumes 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m15-pdes-ivps-error-bounds 65m50-pdes-ibvps-mesh-generation-and-refinement 65m60-pdes-ibvps-finite-elements 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n30-pdes-bvps-finite-elements 65n50-pdes-bvps-mesh-generation-and-refinement
%R 10.1007/978-3-319-67673-9
%T hp-version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
%U https://link.springer.com/book/10.1007%2F978-3-319-67673-9
%X Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios. --
%7 First
%@ 9783319676715 3319676717
@book{cangiani2017hpversion,
abstract = {Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios. --},
added-at = {2021-08-10T02:24:29.000+0200},
address = {Cham},
author = {Cangiani, Andrea and Dong, Zhaonan and Georgoulis, Emmanuil H. and Houston, Paul},
biburl = {https://www.bibsonomy.org/bibtex/20707085952b4c6e04d2a594d55abf264/gdmcbain},
doi = {10.1007/978-3-319-67673-9},
edition = {First},
interhash = {9a1553b49640be02ab8a90872b965015},
intrahash = {0707085952b4c6e04d2a594d55abf264},
isbn = {9783319676715 3319676717},
keywords = {35j25-bvps-2nd-order-elliptic-equations 35l02-first-order-hyperbolic-equations 35m12-pdes-bvps-mixed-type 65-02-numerical-analysis-research-exposition 65m08-pdes-ibvps-finite-volumes 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m15-pdes-ivps-error-bounds 65m50-pdes-ibvps-mesh-generation-and-refinement 65m60-pdes-ibvps-finite-elements 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n30-pdes-bvps-finite-elements 65n50-pdes-bvps-mesh-generation-and-refinement},
publisher = {Springer},
refid = {1002128107},
series = {Springer Briefs in Mathematics},
timestamp = {2021-08-11T08:41:34.000+0200},
title = {hp-version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes},
url = {https://link.springer.com/book/10.1007%2F978-3-319-67673-9},
year = 2017
}