Abstract. We introduce a method for treating general boundary conditions in the finite element method generalizing an approach, due to Nitsche (1971), for approximating Dirichlet boundary conditions. We use Poisson's equations as a model problem and prove a priori and a posteriori error estimates. The method is also compared with the traditional Galerkin method. The theoretical results are verified numerically.
The parameter dependent Brinkman problem, covering a field of problems from the Darcy equations to the Stokes problem, is studied. A mathematical framework is introduced for analyzing the problem. Using this we prove uniform a priori and a posteriori estimates for two families of finite element methods. We also discuss Nitshe's method for imposing boundary conditions.
AMS subject classifications: 65N30
In a previous paper [6] we have extended Nitsche's method [8] for the Poisson equation with general Robin boundary conditions. The analysis required that the solution is in H s , with s > 3/2. Here we give an improved error analysis using a technique proposed by Gudi [5].
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