Related papers: A nodally bound-preserving finite element method f…
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…