相关论文: Finite Element Methods for the Stochastic Allen-Ca…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…
The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…
We propose an unconditionally convergent linear finite element scheme for the stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional noise. By using the Doss-Sussmann technique, we first transform the stochastic LLG…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
This paper proposes a fully discrete method called the symplectic dG full discretization for stochastic Maxwell equations driven by additive noises, based on a stochastic symplectic method in time and a discontinuous Galerkin (dG) method…
In [21] the evolution of hypersurfaces in $\mathbb{R}^{n+1}$ with normal speed equal to a power $k>1$ of the mean curvature is considered and the levelset solution $u$ of the flow is obtained as the $C^0$-limit of a sequence $u^{\epsilon}$…
We establish a unconditional and optimal strong convergence rate of Wong--Zakai type approximations in Banach space norm for a parabolic stochastic partial differential equation with monotone drift, including the stochastic Allen--Cahn…
In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…
We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…
We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…
We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
We prove existence and uniqueness of a solution for the stochastic Allen-Cahn equation with logarithmic potential and multiplicative Wiener noise, under homogeneous Neumann boundary condition. The existence of a solution is obtained in the…
Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial…