An adaptive multilevel approach to parabolic equations in two space dimensions
By: Folkmar A. Bornemann
Contributors: Freie Universität Berlin
Series: Technical report / Konrad-Zuse-Zentrum für Informationstechnik Berlin -- TR 91-7; Technical report (Konrad-Zuse-Zentrum für Informationstechnik Berlin) -- TR 91-7
Publisher: Konrad-Zuse-Zentrum für Informationstechnik Berlin
Published: 1991
Place of publication: Berlin
Language: eng
Number of pages: 136
Subjects: Parabolic Differential equations
Description: Abstract: "A new adaptive multilevel approach for linear parabolic partial differential equations is presented, which is able to handle complicated space geometries, discontinuous coefficients, inconsistent initial data. Discretization in time first (Rothe's method) with order and stepsize control is perturbed by an adaptive finite element discretization of the elliptic subproblems, whose errors are controlled independently. Thus the high standards of solving adaptively ordinary differential equations and elliptic boundary value problems are combined. A theory of time discretization in Hilbert space is developed which yields to an optimal variable order method based on a multiplicative error correction.

The problem of an efficient solution of the singularly perturbed elliptic subproblems and the problem of error estimation for them can be uniquely solved within the framework of preconditioning. A multilevel nodal basis preconditioner is derived, which allows the use of highly nonuniform triangulations. Implementation issues are discussed in detail. Numerous numerical examples in one and two space dimensions clearly show the significant perspectives opened by the new algorithmic approach. Finally an application of the method is given in the area of hyperthermia, a recent clinical method for cancer therapy."
Notes: "Juni 1991."

Thesis (doctoral)--Freie Universität Berlin, 1991.

Includes bibliographical references.