A SUPG Formulation for Solving a Class of Singularly Perturbed Steady Problems in 2D

Date

2020-09-02

Author

Cengizci, Süleyman
Uğur, Ömür
Srinivasan, Natesan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

289
views

0
downloads

In this presentation, approximate solutions of singularly perturbed partial differential equations are examined. It is a well-known fact that the standard Galerkin finite element method (GFEM) experiences some instability problems in obtaining accurate approximations to the solution of convection-dominated equations. Therefore, in this work, the Streamline-Upwind/Petrov-Galerkin (SUPG) method is employed to overcome the instability issues for the numerical solution of these kinds of problems. Furthermore, the stabilized scheme is supported by a shock-capturing technique. Two numerical experiments are provided to compare the results obtained by the GFEM and SUPG methods.

URI

https://hdl.handle.net/11511/93745

Conference Name

The 20th Biennial Computational Techniques and Applications

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations Cengizci, Süleyman (Hindawi Limited, 2017) In thiswork, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, ...
A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity Toraman, Sıtkı Can; Yücel, Hamdullah (2023-04-01) In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are prese...
A Novel Numerical Method for Evaluation of Hypersingular Integrals in Electromagnetics Selcuk, Gokhun; Demir, Oguz; Koç, Seyit Sencer (2015-11-28) In this study we develop a numerical method for evaluation of hypersingular surface integrals, which arise in the solution of electric field integral equation (EFIE) via Nystrom method. Due to the divergent contribution of an infinitesimal area around the singular point, hypersingular integrals are told to be numerically intractable and analytical methods are employed for evaluation of these integrals. In this study we interpret hypersingular integrals as the second order derivative of weakly singular integ...
A quadtree-based adaptively-refined cartesian-grid algorithm for solution of the euler equations Bulkök, Murat; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2005) A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to ...

Citation Formats

S. Cengizci, Ö. Uğur, and N. Srinivasan, “A SUPG Formulation for Solving a Class of Singularly Perturbed Steady Problems in 2D,” presented at the The 20th Biennial Computational Techniques and Applications, Sydney, Avustralya, 2020, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/93745.