The multigroup neutron SP N equations, which are an approximation of the transport equation, used to model nuclear reactor cores. In their steady state, these equations can be written as a source problem or eigenvalue problem. We study resolution those two problems with H 1 -conforming finite element method and Discontinuous Galerkin method, namely Symmetric Interior Penalty method.

In this paper, the direct differentiation method DDM for finite-element FE response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints MPCs . The analytical developments are provided for three different constraint handling methods, namely: 1 the transformation equation method; 2 the Lagrange multiplier method; and 3 the penalty function method. Two n...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

The fictitious domain method with H1-penalty for elliptic problems is considered. We propose a new way to derive the sharp error estimates between the solutions of original elliptic problems and their H1-penalty problems. We find our method of analysis is applicable to parabolic problems while retaining the sharpness of the error estimates. We also prove some regularity theorems for H1-penalty ...

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for linear second-order elliptic reactiondiffusion-advection equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the extension of the error analysis of the hpDGFEM to the case when anisotropic (shape-irregular) elements and anisotropic polynomial degrees are used. ...

SUMMARY The goal of this paper is the implementation of the hybrid V-cycle hierarchical algebraic multilevel methods for the indeenite discrete systems which arise when a mixed nite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indeenite system can be reduced to a symmetric positive deenite system containing the small ...

The goal of this work is to derive and justify a multilevel preconditioner of optimal arithmetic complexity for symmetric interior penalty discontinuous Galerkin finite element approximations of second order elliptic problems. Our approach is based on the following simple idea given in [R.D. Lazarov, P.S. Vassilevski, L.T. Zikatanov, Multilevel preconditioning of second order elliptic discontin...

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and opt...