Error representation formulas and a posteriori error estimates for numerical solutions of hyperbolic conservation laws are considered with specialized variants given for the Godunov finite volume and discontinuous Galerkin finite element methods. The error representation formulas utilize the solution of a dual problem to capture the nonlocal error behavior present in hyperbolic problems. The er...

In this paper, free and forced vibration analysis of functionally graded material cylinders was carried out by mesh-free and finite element method. In this analysis, MLS shape functions are used for approximation of displacement field in the weak form of motion equation and essential boundary conditions are imposed by transformation method. Resulted set of differential equations are solved usin...

Stochastic Galerkin finite element discretisations of PDEs with stochastically nonlinear coefficients lead to linear systems of equations with block dense matrices. In contrast, stochastic Galerkin finite element discretisations of PDEs with stochastically linear coefficients lead to linear systems of equations with block sparse matrices which are cheaper to manipulate and precondition in the f...

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical ex...

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume e...

In this study, the buckling and free vibration of Timoshenko beams resting on variable elastic foundation analyzed by means of a new finite element formulation. The Winkler model has been applied for elastic foundation. A two-node element with four degrees of freedom is suggested for finite element formulation. Displacement and rotational fields are approximated by cubic and quadratic polynomia...

Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and l...

An adaptive discontinuous Galerkin finite element method for linear elasticity problems is presented. We develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials (absence of volume locking). Furthermore, we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes.

This article introduces and analyzes a weak Galerkin mixed finite element method for solving the biharmonic equation. The weak Galerkin method, first introduced by two of the authors (J. Wang and X. Ye) in [52] for second order elliptic problems, is based on the concept of discrete weak gradients. The method uses completely discrete finite element functions and, using certain discrete spaces an...

We present a discontinuous Galerkin method (DGM) for solutions of the Euler equations on Cartesian grids with embedded geometries. Cartesian grid methods can provide considerable computational savings for computationally intensive schemes like the DGM. Cartesian mesh generation is also simplified compared to the body fitted meshes. However, cutting an embedded geometry out of the grid creates c...