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Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
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MC 6460
Keegan Kirk  Applied Math, University of Waterloo
Analysis of a Spacetime Hybridizable Discontinuous Galerkin Method for AdvectionDiffusion Problems on Evolving Domains
Many important applications of fluid mechanics require the solution of timedependent partial differential equations on evolving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact on offshore structures, and arterial blood flow in the human body. In contrast to problems posed on fixed domains, numerical methods for evolving domains must satisfy the Geometric Conservation Law (GCL), a nontrivial feat.
A viable candidate proven to automatically satisfy the GCL is the spacetime discontinuous Galerkin (DG) method, which makes no distinction between spatial and temporal variables. The problem is fully discretized in space and time instead of the typical method of lines treatment of timedependent problems on fixed domains. This leads to an accurate scheme well suited to handle moving and deforming domains, but at a significant increase in computational cost in comparison to traditional timestepping methods. Attempts to rectify this situation have led to the pairing of spacetime DG with the hybridizable discontinuous Galerkin (HDG) method, which was developed solely to reduce the computational expense of DG. The combination of the two methods results in a scheme that retains the highorder spatial and temporal accuracy and geometric flexibility of spacetime DG without the associated computational burden.
In this talk, we perform an a priori analysis of a spacetime HDG method for the nonstationary advectiondiffusion problem posed on a timedependent domain. We discuss the derivation of anisotropic trace and inverse inequalities valid for moving meshes, which are essential tools for our analysis. Stability of the scheme is proven through the satisfaction of an infsup condition. Finally, we discuss the error analysis of the method and derive theoretical rates of convergence.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader