Anna-Margarete Sändig

• The mathematical modelling of problems in science and engineering leads often to partial differential equations in time and space with boundary and initial conditions.The boundary value problems can be written as extremal problems(principle of minimal potential energy), as variational equations (principle of virtual power) or as classical boundary value problems.There are connections concerning existence and uniqueness results between these formulations, which will be investigated using the powerful tools of functional analysis.The first part of the lecture is devoted to the analysis of linear elliptic boundary value problems given in a variational form.The second part deals with the numerical approximation of the solutions of the variational problems.Galerkin methods as FEM and BEM are the main tools. The h-version will be discussed, and an error analysis will be done.Examples, especially from the elasticity theory, demonstrate the methods.