Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

This primer describes the general model independent searches for new physics phenomena beyond the Standard Model of particle physics. First, the motivation for performing general model independent experimental searches for new physics is presented by giving an overview of the current theoretical understanding of particle physics in terms of the Standard Model of particle physics and its shortcomings. Then, the concept and features of general model independent search for new physics at collider based experiments is explained. This is followed by an overview of such searches performed in past high energy physics experiments and the current status of such searches, particularly in the context of the experiments at the LHC. Finally, the future prospects of such general model independent searches, with possible improvements using new tools such as machine learning techniques, is discussed.

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

This primer describes the general model independent searches for new physics phenomena beyond the Standard Model of particle physics. First, the motivation for performing general model independent experimental searches for new physics is presented by giving an overview of the current theoretical understanding of particle physics in terms of the Standard Model of particle physics and its shortcomings. Then, the concept and features of general model independent search for new physics at collider based experiments is explained. This is followed by an overview of such searches performed in past high energy physics experiments and the current status of such searches, particularly in the context of the experiments at the LHC. Finally, the future prospects of such general model independent searches, with possible improvements using new tools such as machine learning techniques, is discussed.