Adaptive Discontinuous Galerkin Methods for Nonlinear Diffusion Convection Reaction Equations

Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations Yücel, Hamdullah (2015-09-01) We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a poste...
Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations UZUNCA, Murat; Karasözen, Bülent; Manguoğlu, Murat (2014-09-04) In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion convection reaction equations. We propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non-linear equations. Numerical examples demonstrate effectiveness of the DGAFEM to damp the spurious oscillations and resolve well the sharp layers occurring in convection dominated non-line...
Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection diffusion equations Yücel, Hamdullah; Benner, Peter (null; 2014-04-11)
Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations Stoll, Martin; Yücel, Hamdullah; Benner, Peter (2018-01-01) In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. ...
Adaptive discontinuous galerkin methods for non-linear reactive flows Uzunca, Murat; Karasözen, Bülent; Department of Mathematics (2014) The aim of this thesis is to solve the convection/reaction dominated non-stationary semi-linear diffusion-convection-reaction problems with internal/boundary layers in an accurate and efficient way using a time-space adaptive algorithm. We use for space discretization the symmetric interior penalty discontinuous Galerkin method, and backward Euler for time discretization. Our main interest is to derive robust residual-based a posteriori error estimators both in space and time. To derive the a posteriori bou...

Citation Formats

B. Karasözen and M. Manguoğlu, “Adaptive Discontinuous Galerkin Methods for Nonlinear Diffusion Convection Reaction Equations,” 2015, vol. 103, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69387.