Error estimates, error bounds, and adaptive refinement in finite-element quantum theory

Journal Article · Wed May 15 00:00:00 EDT 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.3524· OSTI ID:5591916

Fanchiotti, S ^[1]; Rubin, M A ^[2]

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1. Physics Department, New York University, New York, New York 10003 (USA)
2. Physics Department, Rockefeller University, New York, New York 10021 (USA)

We derive a rigorous {ital a} {ital posteriori} bound on the error in energy eigenvalues obtained using {ital C}{sup 1} finite elements, as well as several {ital a} {ital posteriori} error estimates, and test them numerically with potentials of analytically-known eigenspectrum. We also obtain numerical solutions, with error bounds and estimates, for the octic oscillator potential, illustrating the ability of the finite-element method to resolve-nearly degenerate states with extremely narrow splitting. The incorporation of adaptive refinement is shown to reduce the number of degrees of freedom needed to achieve a given level of accuracy.

• DOE Contract Number: AC02-87ER40325
• OSTI ID: 5591916
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
ERRORS
FIELD THEORIES
FINITE ELEMENT METHOD
MECHANICS
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PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SCHROEDINGER PICTURE
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