In this paper we consider stabilized finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three different stabilized methods: the Galerkin least squares method, the continuous interior penalty method, and the discontinuous Galerkin method. We consider both th...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...

A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is solved by an optimized sparse direct (LU factorizatio...

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier–Stokes equations is formulated and analyzed. We prove unconditional stability of proposed scheme. Convergence discrete velocity established by deriving a priori error estimates. Numerical results verify convergence rates.

In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...

The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable discrete Lagrangian. The exact discrete Lagrangian can either be characterized variationally, or in terms of Jacobi’s solution of the Hamilton– Jacobi equation. The...

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in scienc...

A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The based on standard Galerkin finite element method in spatial direction, fractional Crank-Nicolson method, and extrapolation methods temporal direction. novel discrete Grönwall inequality established. Thanks inequality, error estimate of a fully obtained. Several examples are p...

In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of semi-discrete DG were studied. Optimal error estimate method is obtained one-dimensional case, case on both rectangular meshes triangular under certain mesh assumptions. Strong Taylor 2.0 scheme used as...

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models associate with optimization problems characterized by a minimum-residual objective function and nonlinear equality constraints that explicitly enfo...