The stability and approximation properties of Ritz-Volterra projection and applications. II (Q2721766)
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scientific article; zbMATH DE number 1616507
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The stability and approximation properties of Ritz-Volterra projection and applications. II |
scientific article; zbMATH DE number 1616507 |
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11 April 2002
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Ritz-Volterra projections
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convergence
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semidiscrete finite element approximations
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evolution equations
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integrodifferential equations
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Sobolev equation
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equations of viscoelasticity
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optimal order error estimates
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The stability and approximation properties of Ritz-Volterra projection and applications. II (English)
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For part I see ibid. 6, No. 1, 57-76 (1997; Zbl 0888.65117)]. The author investigates in a unified way the convergence of semidiscrete finite element approximations (Ritz-Volterra projections) to various type of evolution equations: parabolic and hyperbolic integrodifferential equations, Sobolev equation, and equations of viscoelasticity. Assuming the existence and uniqueness of sufficiently smooth solutions, the author obtains optimal order error estimates in \(L_p\) and \(W^1_p\) for \(2\leq p\leq\infty\).
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