descriptionPublicationkeyboard_double_arrow_right Article 06 Jul 2015 English Publisher:Springer Science and Business Media LLCJournal:Journal of Scientific Computing, volume 66, pages 1,313-1,333 (issn: 0885-7474, eissn: 1573-7691,

Authors: Gürkan, Ceren; Sala Lardies, Esther; Kronbichler, Martin; Fernández Méndez, Sonia;

doi: 10.1007/s10915-015-0066-8

handle: 10016/45550 , 2117/84274

eXtended Hybridizable Discontinous Galerkin (X-HDG) for Void Problems

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Abstract

A strategy for the Hybridizable Discontinous Galerkin (HDG) solution of problems with voids, inclusions or free surfaces is proposed. It is based on an eXtended Finite Element philosophy with a level-set description of interfaces. Thus, the computational mesh is not required to fit the interface (i.e. the boundary), simplifying and reducing the cost of mesh generation and, in particular, avoiding continuous remeshing for evolving interfaces. Differently to previous proposals for HDG solution with non-fitting meshes, here the computational mesh covers the domain, avoiding extrapolations, and ensuring the robustness of the method. The local problem at elements not cut by the interface, and the global problem, are discretized as usual in HDG. A modified local problem is considered at elements cut by the interface. At every cut element, an auxiliary trace variable on the boundary is introduced, which is eliminated afterwards using the boundary conditions on the interface, keeping the original unknowns and the structure of the local problem solver. An efficient and robust methodology for numerical integration in cut elements, in the context of high-order approximations, is also proposed. Numerical experiments demonstrate how X-HDG keeps the optimal convergence, superconvergence, and accuracy of HDG with no need of adapting the computational mesh to the interface boundary.

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
Universität Augsburg
Germany
Technical University of Munich
Germany

Keywords

moving boundary, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits, Level-sets, interface, moving boundary, Hybridizable Discontinuous Galerkin (HDG), high-order, level-sets, X-FEM, numerical integration, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Interface Moving boundary Hybridizable Discontinuous Galerkin (HDG) High-order Level-sets X-FEM Numerical integration, X-FEM, :65 Numerical analysis::65N Partial differential equations, boundary value problems [Classificació AMS], :Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits [Àrees temàtiques de la UPC], Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Aeronáutica, level-sets, Ingenieurwissenschaften, Boundary value problems for second-order elliptic equations, Moving boundary, numerical experiment, Anàlisi numèrica, convergence, Stability and convergence of numerical methods for boundary value problems involving PDEs, Interface, Hybridizable Discontinuous Galerkin (HDG), high-order, finite element, hybridizable discontinuous Galerkin, Numerical integration, numerical integration, interface, High-order, Numerical analysis, ddc: ddc:620

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