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Galerkin Solution (galerkin + solution)
Selected AbstractsHierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Koen Hillewaert Abstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton,Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd. [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] On discontinuous Galerkin methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003O. C. Zienkiewicz Abstract Discontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present. Several alternatives for treating the diffusion and advective fluxes have been introduced. This report summarizes some of the methods that have been proposed. Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion,reaction problems and advection,diffusion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method. Copyright © 2003 John Wiley & Sons, Ltd. [source] The use of negative penalty functions in solving partial differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2005Sinniah Ilanko Abstract In variational and optimization problems where the field variable is represented by a series of functions that individually do not satisfy the constraints, penalty functions are often used to enforce the constraint conditions approximately. The major drawback with this approach is that the error due to any violation of the constraint is not known. In a recent publication dealing with the Rayleigh,Ritz method it was shown that, by using a combination of positive and negative penalty parameters, any error due to the violation of the constraints may be kept within any desired tolerance. This paper shows that this approach may also be used in solving partial differential equations using a Galerkin's solution to Laplace's equation subject to mixed Neumann and Dirichlet boundary conditions as an example. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||