We propose and study numerically the implicit approximation in time of Navier–Stokes equations by a Galerkin–collocation method combined with inf–sup stable finite element methods space. The conceptual basis approach is establishment direct connection between Galerkin classical collocation methods, perspective achieving accuracy former reduced computational costs terms less complex algebraic sy...

In this paper we derive an algorithm for solving the Stokes{equations for the example of the Driven{Cavity{Problem. We treat the Stokes{equations in the divergence{free weak formulation and show the construction of divergence{free reenable functions, which will be used as trial functions in the Galerkin{method. The system will be solved by means of the preconditioned cg{method. We make use of m...

We apply hp-cloud method to the radial Dirac eigenvalue problem. The difficulty of occurrence of spurious values among the genuine eigenvalues is treated. The method of treatment is based on assuming hp-cloud Petrov-Galerkin scheme to construct the weak formulation of the problem which adds a consistent diffusivity to the variational formulation without deforming the equation. The size of the a...

In this paper, we propose a new characteristics method for the discretization of the two dimensional fluid-rigid body problem in the case where the densities of the fluid and the solid are different. The method is based on a global weak formulation involving only terms defined on the whole fluid-rigid domain. To take into account the material derivative, we construct a special characteristic fu...

In this paper, a central discontinuous Galerkin method is proposed to solve for the viscosity solutions of Hamilton-Jacobi equations. Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation laws. They combine the central scheme and the discontinuous Galerkin method and therefore carry many features of both methods. Since Hamilton-Jacobi equations in general...

This paper presents the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces RT[0] for qu...

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in...

A Petrov-Galerkin discretization is studied of an ultra-weak variational formulation of the convection-diffusion equation in mixed form. To arrive at an implementable method, the truly optimal test space has to be replaced by its projection onto a finite dimensional test search space. To prevent that this latter space has to be taken increasingly large for vanishing diffusion, a formulation is ...

An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions. The use of these functions shows that the weak form can be integrated with conventional Gaussian integration. The MLPG method was evaluated by applying the formulation to a variety of patch test and thin ...

We prove convergence and quasi-optimality of a lowest-order adaptive boundary element method for a weakly-singular integral equation in 2D. The adaptive meshrefinement is driven by the weighted-residual error estimator. By proving that this estimator is not only reliable, but under some regularity assumptions on the given data also efficient on locally refined meshes, we characterize the approx...