On the finite element method for parabolic equations, I; approximation of holomorphic semi-groups1)

Fujita, Hiroshi; Mizutani, Akira

doi:10.2969/jmsj/02840749

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Introduction2

Will Imply Conditions (H2)-(i) (H2)-(ii)1

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1979

2022

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Cited by 60 publications

(27 citation statements)

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“…In the linear case f= 0 it is well known that the error satisfies the estimate H uh(t)-u(t)lb < Ch" t -"/2 (1.5) * To Professor Dr. J.A. Nitsche on the occasion of his sixtieth birthday where the constant C=Ct ][vie depends only on the norm of v in X and # denotes the approximation order of the finite element spaces S h (see Babuska and Fix [3]; Bramble et al [5]; Fujita and Mizutani [7]; Suzuki [30]; Helfrich [9] and Thom6e [32]). Nitsche [22] discusses in connection with the Stefan problem the case where v is a distribution.…”

Section: Introductionmentioning

confidence: 99%

Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data

Helfrich¹

1987

Numer. Math.

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Section: Introductionmentioning

confidence: 99%

Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data

Helfrich¹

1987

Numer. Math.

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“…For the linear homogeneous equation the nonsmooth data situation has been investigated in Blair [2], Helfrich [9], Fujita and Mizutani [6], Bramble, Schatz, Thomée and Wahlbin [4] and later papers (cf. Thomée [23]).…”

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confidence: 99%

Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Nonsmooth Initial Data

Johnson¹,

Larsson²,

Thomée³

et al. 1987

Mathematics of Computation

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Abstract. We consider time-continuous spatially discrete approximations by the Galerkin finite element method of initial-boundary value problems for semilinear parabolic equations with nonsmooth or incompatible initial data. We find that the numerical solution enjoys a gain in accuracy at positive time of essentially two orders relative to the initial regularity, as a result of the smoothing property of the parabolic evolution operator. For higher-order elements the restriction to two orders is in contrast to known optimal order results in the linear case.

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“…Finally, we mention that Fujita and Mizutani [6] have obtained the estimates of the finite element solutions for the following problems:…”

Section: Introductionmentioning

confidence: 98%

On numerical asymptotic behavior of finite element solutions for parabolic equations

Ishihara

1984

Numer. Math.

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On the finite element method for parabolic equations, I; approximation of holomorphic semi-groups1)

Cited by 60 publications

References 14 publications

Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data

Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data

Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Nonsmooth Initial Data

On numerical asymptotic behavior of finite element solutions for parabolic equations

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