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Symmetric discontinuous Galerkin methods for 1-D waves [electronic resource] : Fourier analysis, propagation, observability and applications

자료유형

E-Book(소장)

개인저자

Marica, Aurora. Zuazua, E. (Enrique).

서명 / 저자사항

Symmetric discontinuous Galerkin methods for 1-D waves [electronic resource] : Fourier analysis, propagation, observability and applications / Aurora Marica, Enrique Zuazua.

발행사항

New York, NY : Springer New York : Imprint: Springer, 2014.

형태사항

1 online resource (xvi, 104 p.) : ill.

총서사항

Springer briefs in mathematics,2191-8198

ISBN

9781461458111

요약

This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.

일반주기

Title from e-Book title page.

내용주기

1. Preliminaries -- 2. Discontinuous Galerkin approximations and main results -- 3. Bibliographical notes -- 4. Fourier analysis of the DG methods -- 5. Non-uniform observability for DG approximations of waves -- 6. Filtering mechanisms -- 7. Extensions to other numerical approximation schemes -- 8. Comments and open problems -- A technical proof -- References.

서지주기

Includes bibliographical references.

이용가능한 다른형태자료

Issued also as a book.

일반주제명

Waves --Mathematics. Galerkin methods. Approximation theory.

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URL

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082	0 4	▼a 530.124 ▼2 23
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100	1	▼a Marica, Aurora.
245	1 0	▼a Symmetric discontinuous Galerkin methods for 1-D waves ▼h [electronic resource] : ▼b Fourier analysis, propagation, observability and applications / ▼c Aurora Marica, Enrique Zuazua.
260		▼a New York, NY : ▼b Springer New York : ▼b Imprint: Springer, ▼c 2014.
300		▼a 1 online resource (xvi, 104 p.) : ▼b ill.
490	1	▼a Springer briefs in mathematics, ▼x 2191-8198
500		▼a Title from e-Book title page.
504		▼a Includes bibliographical references.
505	0	▼a 1. Preliminaries -- 2. Discontinuous Galerkin approximations and main results -- 3. Bibliographical notes -- 4. Fourier analysis of the DG methods -- 5. Non-uniform observability for DG approximations of waves -- 6. Filtering mechanisms -- 7. Extensions to other numerical approximation schemes -- 8. Comments and open problems -- A technical proof -- References.
520		▼a This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.
530		▼a Issued also as a book.
538		▼a Mode of access: World Wide Web.
650	0	▼a Waves ▼x Mathematics.
650	0	▼a Galerkin methods.
650	0	▼a Approximation theory.
700	1	▼a Zuazua, E. ▼q (Enrique).
830	0	▼a Springer briefs in mathematics.
856	4 0	▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-1-4614-5811-1
945		▼a KLPA
991		▼a E-Book(소장)

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No.	소장처	청구기호	등록번호	도서상태	반납예정일	예약	서비스
No. 1	소장처 중앙도서관/e-Book 컬렉션/	청구기호 CR 530.124	등록번호 E14030953	도서상태 대출불가(열람가능)	반납예정일	예약	서비스 M

Symmetric discontinuous Galerkin methods for 1-D waves [electronic resource] : Fourier analysis, propagation, observability and applications

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