1. A posteriori Error Estimate - Adaptive method Consider the boundary value problem Weak form Discrete Equation Error bounds ( priori error )

2. A posteriori Error Estimate - Adaptive method Error bounds Basic Idea: Suppose is given tolerance. We want to obtain FEM approximation such that : (1) Relying on the error estimate above we see that (1) will be satisfied if the corresponding FE mesh is chosen so that (2) To determine a mesh satisfying (2) we may proceed as follows: 1)Choose first mesh and compute the corresponding FE solution 1)Using approximate 1)Construct a new mesh by subdividing into four triangles each for which

3. A posteriori Error Estimate - Adaptive method (2) To determine a mesh satisfying (2) we may proceed as follows: 1)Choose first mesh and compute the corresponding FE solution 1)Using approximate 1)Construct a new mesh by subdividing into four triangles each for which Next compute the FE solution on the new mesh and repeat the process until

4. A posteriori Error Estimate - Adaptive method Consider the boundary value problem Weak form Theorem 5.6 ( A posteriori )

5. HW Consider the boundary value problem Theorem 5.6 ( A posteriori ) Solve Start with