Syllabus
Numerical solution can hardly be reliable if we do not know how inaccurate it is. A posteriori error estimates provide the information about the size of the error and therefore they should supplement all numerical solutions.
Besides this, the a posteriori error estimates enable to find the spatial distribution of the error among the computational domain and optimize the computation by adaptive techniques. This course offers an overview of techniques for a posteriori error estimation.
In particular, it covers explicit and implicit residual estimates, hierarchical estimates, estimates based on the postprocessing and goal oriented estimates. (The complementary estimates are covered by the course A posteriori numerical analysis by the equilibrated fluxes.) Based on the example of Poisson equation discretized by the finite element method, we will explain individual techniques and prove their properties.
Annotation
Numerical solutions should always be accompanied by a posteriori error estimates. Besides the qualitative information about the error, they enable to find the spatial distribution of the error and optimize the computation by adaptive techniques.
The course provides an overview of techniques for a posteriori error estimates and compares their properties.