The 15^th Internet Seminar on Evolution Equations is devoted to operator semigroup methods for numerical analysis. Based on the Lax Equivalence Theorem we give an operator theoretic and functional analytic approach to the numerical treatment of evolution equations. The lectures are at a beginning graduate level and only assume basic familiarity with functional analysis, ordinary and partial differential equations, and numerical analysis.

Organised by the European consortium "International School on Evolution Equations", the annual Internet Seminars introduce master-, Ph.D. students and postdocs to varying subjects related to evolution equations. The course consists of three phases.

• In Phase 1 (October-February), a weekly lecture will be provided via the ISEM website. Our aim is to give a thorough introduction to the field, at a speed suitable for master’s or Ph.D. students. The weekly lecture will be accompanied by exercises, and the participants are supposed to solve these problems.

• In Phase 2 (March-May), the participants will form small international groups to work on diverse projects which complement the theory of Phase 1 and provide some applications of it.

• Finally, Phase 3 (3-9 June 2012) consists of the final one-week workshop at the Heinrich–Fabri Institut in Blaubeuren (Germany). There the teams will present their projects and additional lectures will be delivered by leading experts.