Penalty correction method for elliptic boundary value problems
A new finite element method is introduced for approximating elliptic boundary value problems with inhomogeneous Dirichlet boundary conditions. This new method, the penalty correction method, leads to approximations that are optimal in H/sup 1/, L/sup 2/, and negative Sobolev spaces without very stringent assumptions on the approximating subspaces, viz., the subspaces need not satisfy the Dirichlet boundary conditions or inverse properties. Computationally, the method involves solving the same matrix system, corresponding to Babuska's penalty method, for a number of input vectors. Thus, one can take full advantage of matrix decomposition algorithms available. The penalty correction method also gives rise to high-order approximations to the normal derivative of the solution at the boundary without computing normal derivatives.
- Research Organization:
- Brookhaven National Lab., Upton, NY
- OSTI ID:
- 5401322
- Journal Information:
- SIAM J. Numer. Anal.; (United States), Vol. 16:6
- Country of Publication:
- United States
- Language:
- English
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