Related papers: An energy stable and conservative multiplicative d…
In this paper we study the approximation of the distribution of $X_t$ Hilbert--valued stochastic process solution of a linear parabolic stochastic partial differential equation written in an abstract form as $$ dX_t+AX_t dt = Q^{1/2} d W_t,…
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear part of the target system is usually discretized implicitly,…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
In this paper, we investigate numerical methods for solving Nickel-based phase field system related to free energy, including the elastic energy and logarithmic type functionals. To address the challenge posed by the particular free energy…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches…
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
We design, analyze and numerically validate a novel discontinuous Galerkin method for solving the coagulation-fragmentation equations. The DG discretization is applied to the conservative form of the model, with flux terms evaluated by…
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our previous computational work. This paper presents a numerical…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
In this paper, we present a linearly implicit energy-preserving scheme for the Camassa-Holm equation by using the multiple scalar auxiliary variables approach, which is first developed to construct efficient and robust energy stable schemes…
This paper presents high-order Runge-Kutta (RK) discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry. The scheme can preserve a general polytropic equilibrium state and achieve total energy conservation up to…
The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several…
In this work, we develop a novel numerical scheme to solve the classical Keller--Segel (KS) model which simultaneously preserves its intrinsic mathematical structure and achieves optimal accuracy. The model is reformulated into a gradient…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions,…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
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…