Superconvergence of<i>H</i><sup>1</sup>-Galerkin mixed finite element methods for parabolic problems

Tripathy, Madhusmita; Sinha, Rajen Kumar

doi:10.1080/00036810903208163

Cited by 9 publications

(2 citation statements)

References 16 publications

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“…In 1998, [4], the results of the pioneering work done in [16] for the RT method of degree k = 1 for the homogeneous equation with nonsmooth initial data u 0 and smooth domains in R 2 were extended to the case of RT methods of arbitrary degree k. The extension of the results in [13] to this setting was achieved at the same time. In 2009, [23], superconvergence of the so-called semidiscrete H 1 -Galerkin mixed method was obtained for rectangular elements.…”

Section: Introductionmentioning

confidence: 99%

Uniform-in-time superconvergence of HDG methods for the heat equation

Chabaud

Cockburn

2012

Math. Comp.

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We prove that the superconvergence properties of the hybridizable discontinuous Galerkin method for second-order elliptic problems do hold uniformly in time for the semidiscretization by the same method of the heat equation provided the solution is smooth enough. Thus, if the approximations are piecewise polynomials of degree k, the approximation to the gradient converges with the rate h k+1 for k ≥ 0 and the L 2-projection of the error into a space of lower polynomial degree superconverges with the rate log(T /h 2) h k+2 for k ≥ 1 uniformly in time. As a consequence, an elementby-element postprocessing converges with the rate log(T /h 2) h k+2 for k ≥ 1 also uniformly in time. Similar results are proven for the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods.

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Section: Introductionmentioning

confidence: 99%

Uniform-in-time superconvergence of HDG methods for the heat equation

Chabaud

Cockburn

2012

Math. Comp.

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“…Most recently, there are superconvergence results on H 1 -Galerkin mixed finite element method for parabolic problems in Ref. [44] and for second-order elliptic equations in Ref. [45].…”

Section: Introductionmentioning

confidence: 99%