Related papers: Virtual element method for the system of time depe…
We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule…
We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time-stepping scheme.…
We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…
In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…
The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…
This paper proposes a virtual element method (VEM) combined with a second-order implicit-explicit scheme based on the scalar auxiliary variable (SAV) method for the incompressible magnetohydrodynamics (MHD) equations. We employ the BDF2…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations.…