Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler time-discrete scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal $L^2$ error estimates hold without any time-step (convergence) condition, while all previous works require certain time-step condition. Our theoretical results provide a new understanding on commonly-used linearized schemes for nonlinear parabolic equations. The proof is based on a splitting of the error function into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper is applicable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations

An Efficient and Long-Time Accurate Third-Order Algorithm for the Stokes–Darcy System

A third order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. a novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. the scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. the scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. to the authors\u27 knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes–Darcy system possessing its favorable efficiency, stability, and accuracy properties

Time-dependent Stokes-Darcy Flow with Deposition

This thesis investigates two nonlinear systems of time-dependent partial differential equations that model a filtration process. Existence and uniqueness results for the governing equations is established. For each system, a finite element scheme capable of approximating the solutions is investigated. Accompanying numerical experiments corroborate the analytical findings. Finally, an optimization application concerning the design of a filter is discussed and supported with a numerical study

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Aeronautical engineering: A continuing bibliography with indexes (supplement 251)

This bibliography lists 526 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 240)

This bibliography lists 629 reports, articles, and other documents introduced into the NASA scientific and technical information system in May, 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Lectures on Computational Numerical Analysis of Partial Differential Equations

From Chapter 1: The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.https://uknowledge.uky.edu/me_textbooks/1002/thumbnail.jp

Bibliography of Lewis Research Center technical publications announced in 1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1987. All the publications were announced in the 1987 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

The simulation of single phase, compressible fluid flow in fractured petroleum reservoirs using finite elements

Summary in English.Bibliography: leaves 181-193.In this thesis, commonly used equations governing the flow of fluids are reviewed, from first principles where appropriate. The assumptions that are made in the process are critically assessed and their limitations are discussed. The equations deal with flow through a porous and permeable medium, a single fracture, a network of fractures, and with the coupling of the fracture network and blocks of matrix material