Related papers: An Eulerian space-time finite element method for d…
In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity $u$ on a periodically moving $n$-dimensional hypersurface $\Gamma(t) \subset \mathbb{R}^{n+1}$. We prove existence and uniqueness of…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then we give the stability analysis and error estimates for the…
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which…
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
Time-dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in this case is the vectorial wave equation. For the vectorial…
In this paper, we introduce a discontinuous Finite Element formulation on simplicial unstructured meshes for the study of free surface flows based on the fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a new class…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev functions. By introducing numerical one-sided derivatives as…
We propose a globally divergence conforming discontinuous Galerkin (DG) method on Cartesian meshes for {\em curl-type hyperbolic conservation} laws based on directly evolving the face and cell moments of the Raviart-Thomas approximation…
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…