In this thesis, high order accurate discretization schemes for partial differential equations are investigated. In the first paper, the linearized two-dimensional Navier-Stokes equations are considered. A special formulation of the boundary conditions is used and estimates for the solution to the continuous problem in terms of the boundary conditions are derived using a normal mode analysis. Similar estimates are achieved for the discretized equations. For the discretization, a second order finite difference scheme on a staggered mesh is used. In Paper II, the analysis for the second order scheme is used to develop a fourth order scheme for the fully nonlinear Navier-Stokes equations. The fully nonlinear incompressible Navier-Stokes equations in two space dimensions are considered on an orthogonal curvilinear grid. Numerical tests are performed with a fourth order accurate Padé type spatial finite difference scheme and a semi-implicit BDF2 scheme in time. In Papers III-V, a class of high order accurate time-discretization schemes based on the deferred correction principle is investigated. The deferred correction principle is based on iteratively eliminating lower order terms in the local truncation error, using previously calculated solutions, in each iteration obtaining more accurate solutions. It is proven that the schemes are unconditionally stable and stability estimates are given using the energy method. Error estimates and smoothness requirements are derived. Special attention is given to the implementation of the boundary conditions for PDE. The scheme is applied to a series of numerical problems, confirming the theoretical results. In the sixth paper, a time-compact fourth order accurate time discretization for the one- and two-dimensional wave equation is considered. Unconditional stability is established and fourth order accuracy is numerically verified. The scheme is applied to a two-dimensional wave propagation problem with discontinuous coefficients.

Techn. University, Diss., 2007--Darmstadt.

Stuttgart, Univ., Diss., 2007. / Druckausg. beim Hut Verl., München erschienen.

Thesis (M.App.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 224-244). Also available in electronic format on the Internet.

Thèse (D.Eng.)--Université du Québec à Chicoutimi, 2001. / Document électronique également accessible en format PDF. CaQCU

Zugl.: Stuttgart, Univ., Diss., 2009

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (M.Sc.)--Memorial University of Newfoundland, 2002. / Restricted until May 2003. Bibliography: leaves 98-101.

Universiẗat, Diss., 1999--Stuttgart.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xviii, 178 p.; also includes graphics (some col.) Includes bibliographical references (p. 173-178). Available online via OhioLINK's ETD Center