Related papers: Overlapping Localized Exponential Time Differencin…
In this article, we propose a linearized fully-discrete scheme for solving a time fractional nonlocal diffusion-wave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the $L1$ scheme in…
This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…
Cross-domain time series imputation is an underexplored data-centric research task that presents significant challenges, particularly when the target domain suffers from high missing rates and domain shifts in temporal dynamics. Existing…
This paper analyzes a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems with two time fractional derivatives of orders $ \alpha $ and $ \beta $ ($ 0 < \alpha < \beta < 1 $). The stability of this…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
We apply the ultraspherical spectral method to solving time-dependent PDEs by proposing two approaches to discretization based on the method of lines and show that these approaches produce approximately same results. We analyze the…
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for incompatible, time-analytic forcing term in…
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear…
In this article, we consider discrete schemes for a fractional diffusion equation involving a tempered fractional derivative in time. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the…
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum…
The paper is concerned with the derivation and analysis of nonoverlapping domain decomposition for heterogeneous, anisotropic diffusion problems discretized by the finite element cell-centered (FECC) scheme. Differently from the standard…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…
We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multivalued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time…
We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…
We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration…
In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…
In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic…