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  • 1
    Electronic Resource
    Electronic Resource
    The h-p version of the finite element method (1986)
    Springer
    Computational mechanics 1 (1986), S. 21-41 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper is the first of the series of two which analyses the h-p version of the finite element method in two dimensions. It proves the basic approximation results which in part 2 will be generalized and applied in a computational setting. The main result is that the h-p version leads to an exponential rate of convergence when solving problems with piecewise analytic data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00298636
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  • 2
    Electronic Resource
    Electronic Resource
    The h-p version of the finite element method (1986)
    Springer
    Computational mechanics 1 (1986), S. 203-220 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper is the second in the series of two analyzing the h-p version of the finite element method. It generalizes the results of the first part (Guo, Babuska 1986) and presents computational results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00272624
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The finite element method for parabolic equations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 373-406 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396452
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Direct and inverse error estimates for finite elements with mesh refinements (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 447-471 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N15 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The finite element method is used to solve a second order elliptic boundary value problem on a polygonal domain. Mesh refinements and weighted Besov spaces are used to obtain optimal error estimates and inverse theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399326
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  • 5
    Electronic Resource
    Electronic Resource
    Analysis of finite element methods for second order boundary value problems using mesh dependent norms (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 41-62 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a new approach to the analysis of finite element methods based onC 0-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely ralated to theL 2 norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in theL 2 norm and in the 2nd order Sobolev norm — the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01463997
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  • 6
    Electronic Resource
    Electronic Resource
    The finite element method for parabolic equations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 339-371 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396451
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Theh,p andh-p versions of the finite element method in 1 dimension (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 577-612 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting The main emphasis is placed on the analysis when the (exact) solution has singularity of xα-type. The first part analyzes thep-version, the second theh-version and generalh-p version and the final third part addresses the problems of the adaptiveh-p version.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389733
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 97-121 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395874
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  • 9
    Electronic Resource
    Electronic Resource
    Theh, p andh-p versions of the finite element method in 1 dimension (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 613-657 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR:G18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper is the second in the series of three devoted to the detailed analysis of the three, basic versions of the finite element method in one dimensional setting. The first part [1] analyzed thep-version, the present one concentrates on theh andh-p versions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389734
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Generalized p-FEM in homogenization (2000)
    Springer
    Numerische Mathematik 86 (2000), S. 319-375 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. A new finite element method for elliptic problems with locally periodic microstructure of length $\varepsilon 〉0$ is developed and analyzed. It is shown that the method converges, as $\varepsilon \rightarrow 0$ , to the solution of the homogenized problem with optimal order in $\varepsilon$ and exponentially in the number of degrees of freedom independent of $\varepsilon 〉 0$ . The computational work of the method is bounded independently of $\varepsilon$ . Numerical experiments demonstrate the feasibility and confirm the theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00005409
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