Journal ArticleDOI
The effect of numerical integration in finite element methods for nonlinear parabolic equations
TLDR
In this paper, the effect of numerical integration in finite element methods applied to a class of non-linear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered by numerical integration are given.Abstract:
The effect of numerical integration in finite element methods applied to a class of non-linear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal L2 and H1 estimates for the error and its time derivative are established.read more
Citations
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Journal ArticleDOI
The effect of numerical integration in mixed finite element approximation in the simulation of miscible displacement
TL;DR: In this paper, the effect of numerical integration in finite element procedures applied to a nonlinear system of two coupled partial differential equations describing the miscible displacement of one incompressible fluid by another in a porous meduim was considered.
Journal ArticleDOI
Fully discrete IPDG-HMM for multiscale Richards equation of unsaturated flow in porous media
Haitao Cao,Tao Yu,Xingye Yue +2 more
TL;DR: A fully discrete method for the multiscale Richards equation which describes the flow transport in unsaturated heterogeneous porous media is proposed and takes into account not only the fully macro-scale discretization but also the fully micro-scaleDiscretization for local cell problems.
Journal ArticleDOI
The effect of numerical integration in finite element methods for general nonlinear hyperbolic equations
TL;DR: In this article, the effect of numerical integration in finite element methods for general nonlinear hyperbolic equations was considered and sufficient conditions on the quadrature scheme were given to ensure that the order of convergence is unaltered in the presence of such integration.
Journal ArticleDOI
FEM-IDS for a second order strongly damped wave equation with memory
TL;DR: A linear triangular finite element method-implicit difference scheme (FEM-IDS) for the solution of second order strongly damped wave equation (SDWE) with memory on domain with interfaces with sufficient conditions that guarantee the existence of a unique solution is proposed.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
Journal ArticleDOI
A Priori L_2 Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
TL;DR: In this paper, L2 error estimates for the continuous time and several discrete time Galerkin approxima-tions to solutions of some second order nonlinear parabolic partial differential equations are derived.
Journal ArticleDOI
Galerkin Methods for Parabolic Equations
Jim Douglas,Todd F. Dupont +1 more
TL;DR: Galerkin-type methods, both continuous and discrete in time, are considered for approximating solutions of linear and nonlinear parabolic problems and bounds reducing the estimation of the error to questions in approximation theory are derived.
Book ChapterDOI
The combined effect of curved boundaries and numerical integration in isoparametric finite element methods
TL;DR: In this article, the finite element method with isoparametric finite elements is applied to this problem, with curved finite elements along the boundary, in connection with a numerical quadrature scheme which is used to compute the coefficients of the resulting linear system.
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