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Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
The stable and accurate approximation of discontinuities such as shocks on a finite computational mesh is a challenging task. Detection of shocks or strong discontinuities in the flow solution is typically achieved through a priori troubled…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…
A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretizations are established, and the corresponding existence and uniqueness theorem is proved by…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…
The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
In this paper the author reviews a version of the global Galerkin that was developed and applied in a series of earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
This work is devoted to an inverse problem of identifying a source term depending on both spatial and time variables in a parabolic equation from single Cauchy data on a part of the boundary. A Crank-Nicolson Galerkin method is applied to…
Nonlinear dynamics of fluid conveying pipe, rotating with constant velocity about its longitudinal axis is analyzed. Considering boundary conditions and internal damping, the nonlinear equation of motion is derived, and it is discretized…
This paper presents a weak Galerkin (WG) finite element method for linear elasticity on general polygonal and polyhedral meshes, free from convexity constraints, by leveraging bubble functions as central analytical tools. The proposed…
This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear…
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous…
The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive…
This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite…