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Showing 1 to 14 of 14 for “"continuous galerkin"”.
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An adaptive variational multiscale method with discontinuous subscales for aerodynamic flows
… the art in output-based adaptation uses the discontinuous Galerkin (DG) method, which is computationally expensive due to its duplicated degrees of freedom. Existing continuous Galerkin (CG) methods require up to 20 times fewer degrees of freedom, but lack the combination of stability and …
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A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems
A Flexible Galerkin Finite Element Method (FGM) is a hybrid class of finite element methods that combine the usual continuous Galerkin method with the now popular discontinuous Galerkin method (DGM). A detailed description of the formulation of the FGM on a hyperbolic partial differential equation, …
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A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations
… and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved …
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Provably convergent anisotropic output-based adaptation for continuous finite element discretizations
… (MOESS) algorithm, developed by Yano for Discontinuous Galerkin (DG) discretization, is a highly effective method of this class. This work begins with the extension of the MOESS algorithm to Continuous Galerkin (CG) discretization which requires fewer Degrees Of Freedom (DOF) on a given mesh …
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A Continuous/Discontinuous FE Method for the 3D Incompressible Flow Equations
… equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. …
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A fast enriched FEM for Poisson equations involving interfaces
… by employing the finite element method. The continuous Galerkin solution approximations at the interface elements are modified using the enriched basis functions to make sure that the optimal convergence rates are obtained. Here, the FFT is applied in the fast Poisson solver to significantly …
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A projected multigrid method for the solution of non-linear finite element problems on adaptively refined grids
… partial differential equations and systems. A continuous Galerkin finite-element method is combined with locally adaptive mesh refinement and an optimal multigrid solver to achieve this efficiency. The novel contribution of this work lies in the manner in which these two techniques are …
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A stabilized discontinuous Galerkin method for variational embedding of physics-based data
… operators that emanate via embedding of Discontinuous Galerkin ideas in the continuous Galerkin framework provide a unique avenue to embed physics-based data in the modeling and analysis of the system. Physics-based data, either in discrete or in distributed form can be embedded via the …
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On the Application of an Output-based Adaptive, Higher-order Finite Element Method to Sonic Boom Propagation
… employs the Variational Multiscale with Discontinuous Subscales (VMSD) method, integrating Continuous Galerkin (CG) and Discontinuous Galerkin (DG) features, referred to as VMSD-BR2. This approach leverages static condensation to manage computational cost while utilizing DG stabilization …
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Quantification of Spalart-Allmaras Turbulence Modeling Uncertainties for Hypersonic Flows Utilizing Output-Based Grid Adaptation
… high order unstructured meshes using a modified Continuous Galerkin (CG) finite element method (FEM) discretization. The meshes are iteratively adapted by minimizing the error estimate of a given output functional, such as integrated drag or heat flux, over a boundary. The goal of the study is to …
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On the uncertainty quantification and non-linear hyper elastic simulation of biological tissues
… equations are possible, and in the current work Continuous Galerkin (CG) and the Discontinuous Galerkin (DG) approaches are employed. Additionally, due to natural variations in biophysical properties from person to person, uncertainty quantification may be used to ascertain the impact on …
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Spectral hulls: a degree of freedom reducing hp-strategy in space/time
… (p-refinement). Compared to the conventional continuous/discontinuous FEM, this mechanism yields more accurate solutions with smaller DOF. This methodology is validated throughout the dissertation using various methods including Fourier-Chebyshev collocation, Continuous Galerkin (CG), …
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Simulation and design optimization of wave propagation in heterogeneous materials
… In particular, we introduce the multiscale continuous Galerkin and multiscale hybridizable discontinuous Galerkin methods which exploit the inherent structure of the problem by reusing information from repeated subdomains. The efficiency that these approaches provide (reducing degrees of …
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A Unified Framework for Simulating Impact-Induced Detonation of a Combustible Material in an Elasto-Plastic Confiner
A new framework for the computational simulation of problems arising in continuum me- chanics is presented. It is unified in the sense that it can describe all three major phases of matter within the same set of equations. It is able to represent inviscid fluids, Newtonian and non-Newtonian viscous …