Inhalt: Mixed and hybrid finite element methods overcome locking phenomena in computational mechanics and allow for higher order approximations of dual variables like stress or flux rather than primal variables like displacement and pressure [1]. Existence and convergence analysis relies on basic properties of constrained minimization and saddle point problems [1, 2].
More recently, discontinuous Galerkin (DG), discontinuous Petrov-Galerkin (DPG) methods, or corresponding hybrid versions HDG and HPDG have been developed and analyzed, exploiting the same mathematical structures [3, 4, 5, 6]. Combining local mass conservation with arbitrary order these methods have become the method of choice, e.g., in computational porous media flow.
In this seminar, we plan to highlight the basic ideas, pros and cons of these advanced discretization methods for partial differential equations and the mathematical background of their analysis.
Target audience: Students in the Master Course Mathematics or BMS (Phase I)
Prerequisites: Basic knowledge on theory and numerics of elliptic pdes as taught, e.g. in the lecture "Numerik von partiellen Differentialgleichungen (Numerik III)" at FU Berlin