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Digitale Medien

On the approximate solution of nonlinear variational inequalities (1978)

Mittelmann, Hans -Detlef

Springer

Numerische Mathematik 29 (1978), S. 451-462

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ISSN: 0945-3245

Schlagwort(e): AMS(MOS): 65N30, 49D20 ; CR: 5.17, 5.15

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary Nonlinear locally coercive variational inequalities are considered and especially the minimal surface over an obstacle. Optimal or nearly optimal error estimates are proved for a direct discretization of the problem with linear finite elements on a regular triangulation of the not necessarily convex domain. It is shown that the solution may be computed by a globally convergent relaxation method. Some numerical results are presented.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01432881

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Digitale Medien

On the efficient solution of nonlinear finite element equations I (1980)

Mittelmann, Hans Detlef

Springer

Numerische Mathematik 35 (1980), S. 277-291

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ISSN: 0945-3245

Schlagwort(e): AMS(MOS) ; 65N30 ; 65H10 ; 65K10 ; CR: 5.17, 5.15

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01396413

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Digitale Medien

On the efficient solution of nonlinear finite element equations. II (1981)

Mittelmann, Hans Detlef

Springer

Numerische Mathematik 36 (1981), S. 375-387

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ISSN: 0945-3245

Schlagwort(e): AMS(MOS): 65N30, 65K10, 49D20 ; CR: 5.17, 5.15

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary We consider nonlinear variational inequalities corresponding to a locally convex minimization problem with linear constraints of obstacle type. An efficient method for the solution of the discretized problem is obtained by combining a slightly modified projected SOR-Newton method with the projected version of thec g-accelerated relaxation method presented in a preceding paper. The first algorithm is used to approximately reach in relatively few steps the proper subspace of active constraints. In the second phase a Kuhn-Tucker point is found to prescribed accuracy. Global convergence is proved and some numerical results are presented.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01395953

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