Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity

Peer C. Kunstmann; Buyang Li; Christian Lubich

doi:10.1007/s10208-017-9364-x

Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity

Peer C. Kunstmann, Buyang Li, Christian Lubich

Research output: Journal article publication › Journal article › Academic research › peer-review

15 Citations (Scopus)

Abstract

Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Foundations of Computational Mathematics
DOIs	https://doi.org/10.1007/s10208-017-9364-x
Publication status	Accepted/In press - 10 Aug 2017

Keywords

Error bounds
Gradient flow
Maximal parabolic regularity
Nonlinear parabolic equation
Runge–Kutta method
Stability

ASJC Scopus subject areas

Analysis
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

More information

10.1007/s10208-017-9364-x

http://hdl.handle.net/10397/74212

Cite this

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abstract = "Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems.",

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AU - Kunstmann, Peer C.

AU - Li, Buyang

AU - Lubich, Christian

PY - 2017/8/10

Y1 - 2017/8/10

N2 - Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems.

AB - Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems.

KW - Error bounds

KW - Gradient flow

KW - Maximal parabolic regularity

KW - Nonlinear parabolic equation

KW - Runge–Kutta method

KW - Stability

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U2 - 10.1007/s10208-017-9364-x

DO - 10.1007/s10208-017-9364-x

M3 - Journal article

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JO - Foundations of Computational Mathematics

JF - Foundations of Computational Mathematics

SN - 1615-3375

ER -

Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity

Abstract

Keywords

ASJC Scopus subject areas

More information

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