28 citations · 213 across the 31 of their papers we have counts for
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Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation
Bülent Karasözen, Murat Uzunca, Tuğba Küçükseyhan
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) eq…
Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation
Murat Uzunca, Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu
We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization f…
Optimal Control of Convective FitzHugh-Nagumo Equation
Murat Uzunca, Tuğba Küçükseyhan, Hamdullah Yücel +1
We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includ…
Structure preserving integration and model order reduction of skew-gradient reaction-diffusion systems
Bülent Karasözen, Tuğba Küçükseyhan, Murat Uzunca
Activator-inhibitor FitzHugh-Nagumo (FHN) equation is an example for reaction-diffusion equations with skew-gradient structure. We discretize the FHN equation using symmetric inter…
Energy stable interior penalty discontinuous Galerkin finite element method for Cahn-Hilliard equation
Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu, Murat Uzunca
An energy stable conservative method is developed for the Cahn--Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conservin…
Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism
Bülent Karasözen, Murat Uzunca
In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in Péclet number) elliptic error estimator in…
A Matlab Tutorial for Diffusion-Convection-Reaction Equations using DGFEM
Murat Uzunca, Bülent Karasözen
We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code em…