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11	hp-Adaptive Discontinuous Galerkin Finite Element In Time For Rotor Dynamics Problem Gudla, Pradeep Kumar 07 1900 (has links) (PDF) No description available. Airplanes - Rotors Rotor Dynamics Finite Element Method Rotors (Helicopters) Discontinuous Galerkin Methods Helicopter Rotor Blades Helicopter Rotor Dynamics Galerkin Finite Element Aeronautics
12	Anisotropic mesh refinement in stabilized Galerkin methods Apel, Thomas, Lube, Gert 30 October 1998 (has links) The numerical solution of the convection-diffusion-reaction problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least squares type accomodates diffusion-dominated as well as convection- and/or reaction- dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is accomplished using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used. info:eu-repo/classification/ddc/510 ddc:510
13	Anisotropic mesh refinement for singularly perturbed reaction diffusion problems Apel, Th., Lube, G. 30 October 1998 (has links) The paper is concerned with the finite element resolution of layers appearing in singularly perturbed problems. A special anisotropic grid of Shishkin type is constructed for reaction diffusion problems. Estimates of the finite element error in the energy norm are derived for two methods, namely the standard Galerkin method and a stabilized Galerkin method. The estimates are uniformly valid with respect to the (small) diffusion parameter. One ingredient is a pointwise description of derivatives of the continuous solution. A numerical example supports the result. Another key ingredient for the error analysis is a refined estimate for (higher) derivatives of the interpolation error. The assumptions on admissible anisotropic finite elements are formulated in terms of geometrical conditions for triangles and tetrahedra. The application of these estimates is not restricted to the special problem considered in this paper. info:eu-repo/classification/ddc/510 ddc:510 elliptic boundary value problems Galerkin finite element methods anisotropic mesh refinement MSC 65N30 MSC 65N50 MSC 35J25
14	Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods and Boundary Element Methods Of, Günther, Rodin, Gregory J., Steinbach, Olaf, Taus, Matthias 19 October 2012 (has links) This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.:1. Introduction 2. Model Problem and Background 3. New Coupling Methods 4. Stability and Error Analysis 5. Numerical Examples 6. Summary A. Appendix info:eu-repo/classification/ddc/518 ddc:518 Kopplung, Randelementmethode
15	Numerická analýza aproximace nepolygonální hranice u nespojité Galerkinovy metody / Numerical analysis of approximation of nonpolygonal domains for discontinuous Galerkin method Klouda, Filip January 2012 (has links) Title: Numerical analysis of approximation of nonpolygonal domains for discon- tinuous Galerkin method Author: Filip Klouda Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., KNM MFF UK Abstract: In this work we use the discontinuous Galerkin finite element method for the semidiscretization of a nonlinear nonstationary convection-diffusion pro- blem defined on a nonpolygonal two-dimensional domain. Using so called appro- ximating curved elements we define a piecewise polynomial approximation of the boundary of the domain and a space on which we search for a solution. We study the convergence of the method considering a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The obtained results allow us to derive an error estimate for the Discontinuous Galer- kin method employing the approximating curved elements. This estimate depends on the order of the approximation of the solution and also on the order of the approximation of the boundary. We describe one possibility of the construction of the approximating curved elements with the aid of a polynomial mapping given by an interpolation of points on the boundary. We present numerical experiments. Keywords: nonlinear convection-diffusion equation, discontinuous...
16	Adaptive Mesh Refinement Solution Techniques for the Multigroup SN Transport Equation Using a Higher-Order Discontinuous Finite Element Method Wang, Yaqi 16 January 2010 (has links) In this dissertation, we develop Adaptive Mesh Refinement (AMR) techniques for the steady-state multigroup SN neutron transport equation using a higher-order Discontinuous Galerkin Finite Element Method (DGFEM). We propose two error estimations, a projection-based estimator and a jump-based indicator, both of which are shown to reliably drive the spatial discretization error down using h-type AMR. Algorithms to treat the mesh irregularity resulting from the local refinement are implemented in a matrix-free fashion. The DGFEM spatial discretization scheme employed in this research allows the easy use of adapted meshes and can, therefore, follow the physics tightly by generating group-dependent adapted meshes. Indeed, the spatial discretization error is controlled with AMR for the entire multigroup SNtransport simulation, resulting in group-dependent AMR meshes. The computing efforts, both in memory and CPU-time, are significantly reduced. While the convergence rates obtained using uniform mesh refinement are limited by the singularity index of transport solution (3/2 when the solution is continuous, 1/2 when it is discontinuous), the convergence rates achieved with mesh adaptivity are superior. The accuracy in the AMR solution reaches a level where the solution angular error (or ray effects) are highlighted by the mesh adaptivity process. The superiority of higherorder calculations based on a matrix-free scheme is verified on modern computing architectures. A stable symmetric positive definite Diffusion Synthetic Acceleration (DSA) scheme is devised for the DGFEM-discretized transport equation using a variational argument. The Modified Interior Penalty (MIP) diffusion form used to accelerate the SN transport solves has been obtained directly from the DGFEM variational form of the SN equations. This MIP form is stable and compatible with AMR meshes. Because this MIP form is based on a DGFEM formulation as well, it avoids the costly continuity requirements of continuous finite elements. It has been used as a preconditioner for both the standard source iteration and the GMRes solution technique employed when solving the transport equation. The variational argument used in devising transport acceleration schemes is a powerful tool for obtaining transportconforming diffusion schemes. xuthus, a 2-D AMR transport code implementing these findings, has been developed for unstructured triangular meshes. Adaptive Mesh Refinement Multigroup SN transport equation Discrete Ordinates Higher-order Finite Element Method Diffusion Synthetic Acceleration Variational argument hp-type unstructured mesh Xuthus
17	Discontinuous Galerkin Finite Element Method for the Nonlinear Hyperbolic Problems with Entropy-Based Artificial Viscosity Stabilization Zingan, Valentin Nikolaevich 2012 May 1900 (has links) This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization. CFD Computational Fluid Dynamics DG FEM Entropy Viscosity Entropy Viscosity Finite Elements, Euler equations compressible Euler equations Higher-order numerical method Navier-Stokes deal.II adaptive mesh KPP rotating wave CG CG FEM continuous Galerkin artificial viscosity entropy-based artificial viscosity Riemann number 12 mach 3 flow wind tunnel circular explosion forward facing step Burgers' equation linear transport equation fluid flow flow fluid perfect gas ideal gas 1D 2D

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