Related papers: Automatic Variationally Stable Analysis for Finite…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…
The Adaptive Stabilized Finite Element method (AS-FEM) developed in Calo et. al. combines the idea of the residual minimization method with the inf-sup stability offered by the discontinuous Galerkin (dG) frameworks. As a result, the…
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV)…
We propose and analyze a time-stepping discontinuous Petrov-Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence,…
Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We analyse a Eulerian Finite Element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations using the CutFEM approach with inf-sup stable Taylor-Hood elements for the spatial discretisation. This is…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
A priori analysis for a generalized local projection stabilized finite element approximations for the solution of an advection-reaction equation is presented in this article. The stability and a priori error estimates are established for…
We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput.…
In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the…
We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\subset$ R d , d = 2 or…
In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the…