Adaptive finite element grid generation and extension for elliptic problems posed on unbounded domains

Technical Report · Tue May 01 04:00:00 EDT 1984

OSTI ID:6821440

Seager, M K

This dissertation concerns the analysis, approximation and algorithmic development for the numerical solution of a second order linear elliptic boundary value problem posed on an infinite domain in R/sup 3/. In presenting the theoretical background, using the weighted Sobolev spaces introduced by Cantor (1981) the use of different boundary conditions on truncated domains was analyzed. It was proven that, under more stringent requirements on the data, the Robin boundary condition yielded solutions on the truncated domains that converged in L/sup 2/,H/sup 1/ and energy norms to the true solution on the unbounded domain. If the domain over which the error norms are calculated is fixed or the data have even faster fall off, the convergence rate increases a full degree. These asymptotic convergence results deal with the continuous solution on the bounded domain. That is to say, discretization error for an approximate solution was not considered. 53 references.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6821440
• Report Number(s): UCRL-53519; ON: DE84012134
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
FINITE ELEMENT METHOD
MATHEMATICAL LOGIC
MESH GENERATION
NUMERICAL SOLUTION