Accession Number:

ADA288358

Title:

Adaptive Finite Element Method II: Error Estimation.

Descriptive Note:

Final rept.,

Corporate Author:

ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS

Personal Author(s):

• Coyle, J. M.
• Flaherty, J. E.

Report Date:

1994-09-01

Pagination or Media Count:

31.0

Abstract:

An adaptive finite element method is developed to solve initial boundary value problems for vector systems of parabolic partial differential equations in one space dimension and time. The differential equations are discretized in space using piecewise linear finite element approximations. Superconvergence properties and quadratic polynomials are used to derive a computation ally inexpensive approximation to the spatial component of the error. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. Computational results indicate that these approximations converge to the exact discretization errors as the mesh is refined.

Descriptors:

• *FINITE ELEMENT ANALYSIS
• *ERROR ANALYSIS
• *BOUNDARY VALUE PROBLEMS
• LINEAR SYSTEMS
• SPATIAL DISTRIBUTION
• COMPUTATIONS
• ESTIMATES
• INTEGRATION
• APPROXIMATION(MATHEMATICS)
• POLYNOMIALS
• ADAPTIVE SYSTEMS
• PARABOLAS
• PARTIAL DIFFERENTIAL EQUATIONS
• QUADRATIC EQUATIONS
• CONVERGENCE
• VECTOR ANALYSIS

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE