1,721,044 research outputs found
Stabilized Mixed Methods for the Stokes Problem
No full textBrezzi, Franco; Douglas, Jr., J.. (1987). Stabilized Mixed Methods for the Stokes Problem. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4673
Recent results in the treatment of subgrid scales
No full textIn recent times, several attempts have been made to recover some information from the subgrid scales and transfer them to the computational scales. Many stabilising techniques can also be considered as part of this effort. We discuss here a framework in which some of these attempts can be set and analysed
The three-field formulation for elasticity problems
No full textThe three-field decomposition method is particularly suited for decompositions with nonmatching grids. It corresponds to introduce an additional grid (usually uniform, or “easy”) at the interface. The unknown is then represented independently in each subdomain and on the interface. The matching between its value in each subdomain and on the interface is provided by suitable Lagrange multipliers. Here we discuss the main features of the method for a linear
three-dimensional elasticity problem, in the simplest case of two subdomains. An easy numerical test to check whether the inf-sup conditions (necessary for the stability) are satisfied is also presented
Functional Analysis, Functional Spaces, Partial Differential Equations
No full textchapters 1-3 of "Finite Element Handbook", Kardestuncer & Norris ed
A nonconforming element for the Reissner-Mindlin plate
No full textWe develop a locking free nonconforming element for the Reissner-Mindlin plate using Discontinuous Galerkin techniques, and prove optimal error estimates
Error estimates for the three-field formulation with bubble stabilization
No full textIn this paper we prove convergence and error estimates for the so-called 3-field formulation using piecewise linear finite elements stabilized with boundary bubbles. Optimal error bounds are proved in L^2 and in the broken H^1 norm for the internal variable u, and in suitable weighted L^2 norms for the other two interface variable
A minimal stabilisation procedure for mixed finite element methods.
No full textStabilisation methods are often used to circumvent the difficulties
associated with the stability of mixed finite element methods. Stabilisation
however also means an excessive amount of dissipation or the loss of nice
conservation properties. It would thus be desirable to reduce these
disadvantages to a minimum. We present a general framework, not restricted to
mixed methods, that permits to introduce a minimal stabilising term and hence a
minimal perturbation with respect to the original problem. To do so, we rely
on the fact that some part of the problem is stable and should not be modified.
Sections 2 and 3 present the method in an abstract framework. Section 4 and 5
present two classes of stabilisations for the inf-sup condition in mixed
problems. We present many examples, most arising from the discretisation of
flow problems. Section 6 presents examples in which the stabilising terms is
introduced to cure coercivity problems
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