Estimating spatial and parameter error in parameterized nonlinear reaction-diffusion equations.

Journal Article · Sun May 01 00:00:00 EDT 2005 · Proposed for publication in Communications in Numerical Methods in Engineering.

OSTI ID:971833

Carey, Graham F ^[1]; Carnes, Brian R ^[1]

---

1. University of Texas at Austin, Austin TX

A new approach is proposed for the a posteriori error estimation of both global spatial and parameter error in parameterized nonlinear reaction-diffusion problems. The technique is based on linear equations relating the linearized spatial and parameter error to the weak residual. Computable local element error indicators are derived for local contributions to the global spatial and parameter error, along with corresponding global error indicators. The effectiveness of the error indicators is demonstrated using model problems for the case of regular points and simple turning points. In addition, a new turning point predictor and adaptive algorithm for accurately computing turning points are introduced.

• Research Organization: Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 971833
• Report Number(s): SAND2005-3133J; TRN: US201004%%221
• Journal Information: Proposed for publication in Communications in Numerical Methods in Engineering., Journal Name: Proposed for publication in Communications in Numerical Methods in Engineering.
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ALGORITHMS
ERRORS
NONLINEAR PROBLEMS
CHEMICAL REACTIONS
DIFFUSION
PARAMETRIC ANALYSIS
ADAPTIVE SYSTEMS