On a Finite Element Method for Solving the Neutron Transport Equation
P. Lesaint,P. A. Raviart +1 more
- 01 Jan 1974
- pp 1-40
TL;DR: The finite element method is studied which provides an effective way for numerically solving such problems and an algorithm for computing the approximate solution is given.
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Abstract: Publisher Summary This chapter discusses the finite element method for solving the neutron transport equation and spatial discretization. It also discusses the numerical approximation of a problem by a finite element method using triangular or quadrilateral elements and other methods for solving the neutron transport equation. The discrete Galerkin method is equivalent to some implicit Runge-Kutta method. The existence and uniqueness of the approximate solution and an algorithm for computing the approximate solution is given. In the chapter, the finite element method is studied which provides an effective way for numerically solving such problems.
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Citations
Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
Sergio Rojas,David Pardo,David Pardo,David Pardo,Pouria Behnoudfar,Victor M. Calo,Victor M. Calo +6 more
TL;DR: This work proposes and analyzes a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms and illustrates the performance of this goal- oriented adaptive strategy on advection-diffusion-reaction problems.
From Godunov to a unified hybridized discontinuous Galerkin framework for partial differential equations
TL;DR: The purpose is to present a step-by-step construction of various HDG methods, including the most economic ones with least trace unknowns, by exploiting the particular structure of the underlying PDEs.
A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case
TL;DR: A high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic–elastic media and experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions are provided.
A Discontinuous Subgrid Eddy Viscosity Method for the Time-Dependent Navier--Stokes Equations
Songul Kaya,Béatrice Rivière +1 more
TL;DR: An error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier--Stokes equations is provided.
hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
Hermann Brunner,Dominik Schötzau +1 more
TL;DR: It is shown that start-up singularities can be resolved at exponential rates of convergence by using geometrically graded time-step bounds in the Galerkin time-stepping method.
References
Implicit Runge-Kutta processes
TL;DR: In this article, it is assumed that the Taylor expansions for y and y may be terminated at any term with an error of the same order as the first term omitted, and all derivatives exist and are continuous.
Interpolation theory over curved elements, with applications to finite element methods
TL;DR: In this article, a general theory for obtaining asymptotic estimates of the form ∥ u − Πu ∥ Hm ( K ) = O ( h k + 1− m ).
294
The combined effect of curved boundaries and numerical integration in isoparametric finite element methods
Philippe G. Ciarlet,P.-A. Raviart +1 more
- 01 Jan 1972
TL;DR: In this article, the finite element method with isoparametric finite elements is applied to this problem, with curved finite elements along the boundary, in connection with a numerical quadrature scheme which is used to compute the coefficients of the resulting linear system.
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