Related papers: A discontinuous Galerkin formulation for a strain …
We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…
This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…
High order accurate and explicit time-stable solvers are well suited for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfaces and nonlinear boundary and interface conditions,…
In this paper, a new stabilized discontinuous Galerkin method within a new function space setting is introduced, which involves an extra stabilization term on the normal fluxes across the element interfaces. It is different from the general…
Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce…
We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…
In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…
A nodal Discontinuous Galerkin (DG) method is derived for the analysis of time-domain (TD) scattering from doubly periodic PEC/dielectric structures under oblique interrogation. Field transformations are employed to elaborate a formalism…
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local time-stepping near boundaries, the method overcomes the…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
Flexoelectricity - the generation of electric field in response to a strain gradient - is a universal electromechanical coupling, dominant only at small scales due to its requirement of high strain gradients. This phenomenon is governed by…
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and…
This paper introduces a weak Galerkin (WG) finite element method for the Stokes equations in the primary velocity-pressure formulation. This WG method is equipped with stable finite elements consisting of usual polynomials of degree $k\ge…
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard…
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order…
In this paper, we consider multiscale methods for nonlinear elasticity. In particular, we investigate the Generalized Multiscale Finite Element Method (GMsFEM) for a strain-limiting elasticity problem. Being a special case of the naturally…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…