相关论文: Ultraspherical Spectral Method for Block Copolymer…
This work performs the convergence analysis of the polytopal nodal discretisation of contact-mechanics (with Tresca friction) recently introduced in [18] in the framework of poro-elastic models in fractured porous media. The scheme is based…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
We compare two theoretical approaches to dielectric diblock copolymer melts in an external electric field. The first is a relatively simple analytic expansion in the relative copolymer concentration, and includes the full electrostatic…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
We investigate a coupled hyperbolic-parabolic system modeling thermoelastic diffusion (resp. thermo-poroelasticity) in plates, consisting of a fourth-order hyperbolic partial differential equation for plate deflection and two second-order…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The objective of this paper is twofold. First, we propose two composable block solver methodologies to solve the discrete systems that arise from finite element discretizations of the double porosity/permeability (DPP) model. The DPP model,…
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
This paper presents an auto-stabilized weak Galerkin (WG) finite element method for the Biot's consolidation model within the classical displacement-pressure two-field formulation. Unlike traditional WG approaches, the proposed scheme…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…
In this work, we consider the discretization of nonlinear hyperbolic systems in nonconservative form with the high-order discontinuous Galerkin spectral element method (DGSEM) based on collocation of quadrature and interpolation points…
We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…