Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition

2008 ◽  
Vol 23 (4) ◽  
pp. 455-462 ◽  
Author(s):  
Dong-yang Shi ◽  
Zhi-yan Li
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Hyperbolic Equations ◽  
The Finite Element Method ◽  
Nonlinear Hyperbolic Equations ◽  
Element Method

Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

scholarly journals A finite element method for a diffusion equation with constrained energy and nonlinear boundary conditions

1993 ◽  
Vol 35 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Amiya K. Pani
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Diffusion Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Boundary Conditions ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Finite Element Galerkin Method

AbstractA finite element Galerkin method for a diffusion equation with constrained energy and nonlinear boundary condition is analysed and optimal error estimates in L2 and L∞-norms are derived. These results improve upon previously derived estimates by Cannon et al. [4].

The finite element method for solving the oblique derivative boundary value problems in geodesy

2020 ◽  
Author(s):  
Marek Macák ◽  
Zuzana Minarechová ◽  
Róbert Čunderlík ◽  
Karol Mikula
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Satellite Orbits ◽  
The Finite Element Method ◽  
Hexahedral Elements ◽  
Grid Points ◽  
Element Method

<p>We present a novel approach to the solution of the geodetic boundary value problem with an oblique derivative boundary condition by the finite element method. Namely, we propose and analyse a finite element approximation of a Laplace equation holding on a domain with an oblique derivative boundary condition given on a part of its boundary. The oblique vector in the boundary condition is split into one normal and two tangential components and derivatives in tangential directions are approximated as in the finite difference method. Then we apply the proposed numerical scheme to local gravity field modelling. For our two-dimensional testing numerical experiments, we use four nodes bilinear quadrilateral elements and for a three-dimensional problem, we use hexahedral elements with eight nodes. Practical numerical experiments are located in area of Slovakia that is given by grid points located on the Earth's surface with uniform spacing in horizontal directions. Heights of grid points are interpolated from the SRTM30PLUS topography model. An upper boundary is in the height of 240 km above a reference ellipsoid WGS84 corresponding to an average altitude of the GOCE satellite orbits. Obtained solutions are compared to DVRM05.</p>

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