In this paper we investigate the relationship between the continuous and the discontinuous Galerkin methods for elliptic problems. In particular, we show that the continuous Galerkin method can be interpreted as the limit of a discontinuous Galerkin method when a stabilization parameter tends to innnity. Based on this observation we derive a method for computing a conservative approximation of ...

In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

We extend the results on minimal stabilization of Burman and Stamm (”Minimal stabilization of discontinuous Galerkin finite element methods for hyperbolic problems”, J. Sci. Comp., DOI: 10.1007/s10915-007-9149-5) to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the ...

We apply in this paper the weak Galerkin method to the second order parabolic differential equations based on a discrete weak gradient operator. We establish both the continuous time and the discrete time weak Galerkin finite element schemes, which allow using the totally discrete functions in approximation space and the finite element partitions of arbitrary polygons with certain shape regular...

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. Standard boundary or finite element methods, with a piecewise polynomial approximation space, have a computational cost that grows linearly with respect to the frequency of the incident wave. Recently ChandlerWilde and Langdon proposed a novel Galerkin boundary element method fo...

In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier–Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproble...

The application of a new nonlinear robust control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Isaacs equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solve...