10 papers · 1 filter
Parametric elliptic reconstructions and a posteriori error estimates for parabolic partial differential equations with small randomness in a Robin boundary condition
Nakidi Shravani, Gujji Murali Mohan Reddy, Amiya Kumar Pani +1
We obtain reliable a posteriori residual-based error estimates for parabolic partial differential equations with small randomness in a Robin-type boundary condition. The uncertaint…
Parameter-robust well-posedness and discretisation for coupled Darcy--Forchheimer and advection-diffusion-reaction equations
Rishi Das, Harsha Hutridurga, Amiya K. Pani +1
We adapt the recent theory for unique solvability of perturbed saddle-point problems in Banach spaces to the case of parameter-independent stability bounds. This also constitutes a…
Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations
Bikram Bir, Amiya K. Pani
Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fu…
Robust stability and preconditioning of Darcy-Forchheimer equations
Rishi Das, Harsha Hutridurga, Amiya K. Pani +1
We derive parameter-robust quasi-optimal error estimates for mixed finite element methods for the nonlinear Darcy--Forchheimer equations with mixed boundary conditions. Using the f…
Error analysis with exponential decay estimates for a fully discrete approximation of a class of strongly damped wave equations
Krishan Kumar, P. Danumjaya, Anil Kumar +1
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions c…
Error Estimates for Discontinuous Galerkin Approximations to the Vlasov-Unsteady Stokes System
Harsha Hutridurga, Krishan Kumar, Amiya K. Pani
In the first part of this paper, uniqueness of strong solution is established for the Vlasov-unsteady Stokes problem in 3D. The second part deals with a semi discrete scheme, which…