This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

This book is an introduction to a family of discontinuous Galerkin (DG) methods applied to
some steady-state and time-dependent model problems. A special effort was made to have …

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …

A combination of ideas in least-squares finite element methods with those of hybridized
methods recently led to discontinuous Petrov--Galerkin (DPG) finite element methods. They …

This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on
general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element …

We propose a simulation technique for elastically deformable objects based on the
discontinuous Galerkin finite element method (DG FEM). In contrast to traditional FEM, it …

It is important to develop fast yet accurate numerical methods for seismic wave propagation
to characterize complex geological structures and oil and gas reservoirs. However, the …

In this study, the generalized finite difference method (GFDM) was used to stably and
accurately solve two-dimensional (2D) inverse Cauchy problems in linear elasticity by using …

Within this work, we develop a phase-field description for simulating fractures in nearly
incompressible materials. It is well-known that low-order approximations generally lead to …

This article proposes a nonconforming immersed finite element (IFE) method for solving
planar elasticity interface problems with structured (or Cartesian) meshes even if the …