“This book should be very useful to Ph.D students and researchers who are eager to explore and understand the mathematical analysis of DGFEMs on polytopic meshes for second-order elliptic equations. The presentation is lucid and the book provides an extensive list of references in the area.” (Neela Nataraj, Mathematical Reviews, October, 2018)

• 1 Introduction.- 2 Introduction to Discontinuous Galerkin Methods.- 3 hp–Inverse and Approximation Estimates.- 4 DGFEMs for Pure Diffusion Problems.- 5 DGFEMs for second–order PDEs of mixed–type.- 6 Implementation Aspects.- 7 Adaptive Mesh Refinement.- 8 Summary and Outlook.- References.

“This book should be very useful to Ph.D students and researchers who are eager to explore and understand the mathematical analysis of DGFEMs on polytopic meshes for second-order elliptic equations. The presentation is lucid and the book provides an extensive list of references in the area.” (Neela Nataraj, Mathematical Reviews, October, 2018)

• 1 Introduction.- 2 Introduction to Discontinuous Galerkin Methods.- 3 hp–Inverse and Approximation Estimates.- 4 DGFEMs for Pure Diffusion Problems.- 5 DGFEMs for second–order PDEs of mixed–type.- 6 Implementation Aspects.- 7 Adaptive Mesh Refinement.- 8 Summary and Outlook.- References.