Mixed Variational Principles and Robust Finite Element Design of Gradient Plasticity at Finite Strains

Mixed Finite Element Methods

A new mixed nite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity. This new mixed discretization ts the geometric shapes of the discontinuity of the rough coeecients and domain boundaries well. This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas's mixed ...

Mixed Finite Element Methods

Finite element methods in which two spaces are used to approximate two different variables receive the general denomination of mixed methods. In some cases, the second variable is introduced in the formulation of the problem because of its physical interest and it is usually related with some derivatives of the original variable. This is the case, for example, in the elasticity equations, where...

Some Aspects of a Discontinuous Galerkin Formulation for Gradient Plasticity at Finite Strains

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this we show that the geometric nonlinearities via the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via the energy dissipation the spatial...

Expanded Mixed Finite Element Methods

We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its ux (the coeecient times the gradient). Based on this formulation, mixed nite element approximations of the second-order elliptic problems ar...