5 papers
Long-time &-stability of the Family of DLN Methods for the Two-dimensional Incompressible Navier-Stokes Equations
Isabel Barrio Sanchez, Wenlong Pei, Catalin Trenchea
In this report, we study the long-time stability of the family of one-leg DLN methods for the two-dimensional incompressible Navier-Stokes equations. The family of DLN methods (wit…
Long-Time H1-Stability of the Cauchy One-Leg Theta-Method for the Navier-Stokes Equations
Isabel Barrio Sanchez, Catalin Trenchea, Wenlong Pei
In this paper we study the long-time stability of the Cauchy one-leg theta-methods for the two-dimensional NavierStokes equations. We establish the uniform dissipativity in H^1, in…
A High-Accuracy Symplectic Scheme for a nonlinear transport problem
Farjana Siddiqua, Catalin Trenchea
We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process.We prove stability and error estimates for both c…
Fourth-Order Compact FDMs for Steady and Time-Dependent Nonlinear Convection-Diffusion Equations
Qiwei Feng, Catalin Trenchea
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonline…
Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables
Zhen Yao, Catalin Trenchea, Wenlong Pei
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm…