Related papers: A Galerkin approximation scheme for the mean corre…
In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…
Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite dimensional Galerkin approximations is established and the convergence rate of the Galerkin approximations to the solution of the…
In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers' system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov…
We establish weak convergence rates for spectral Galerkin approximations of the stochastic viscous Burgers equation driven by additive trace-class noise. Our results complement the known results regarding strong convergence; we obtain…
We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a…
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for…
We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a…
The tempered fractional diffusion equation could be recognized as the generalization of the classic fractional diffusion equation that the truncation effects are included in the bounded domains. This paper focuses on designing the high…
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…
We study dynamical Galerkin schemes for evolutionary partial differential equations (PDEs), where the projection operator changes over time. When selecting a subset of basis functions, the projection operator is non-differentiable in time…
We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in space, a…
We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order $\alpha (1<\alpha<2)$ defined through the fractional Laplacian. The fractional operator of order $\alpha$ is expressed as a…
This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's…
To model wave propagation in inhomogeneous media with frequency-dependent power-law attenuation, it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in…
This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in the spatial…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered…
This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…
In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the…