We consider mixed nite element methods for second order elliptic equations on non-matching multiblock grids. A mortar nite element space is introduced on the non-matching interfaces. We approximate in this mortar space the trace of the solution, and we impose weakly a continuity of ux condition. A standard mixed nite element method is used within the blocks. Optimal order convergence is shown f...

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

We introduce provably unconditionally stable mixed variational methods for phasefield models. Our formulation is based on a mixed finite element method for space discretization and a new second-order accurate time integration algorithm. The fully-discrete formulation inherits the main characteristics of conserved phase dynamics, namely, mass conservation and nonlinear stability with respect to ...

In the paper we discuss two versions of mortar finite element methods applied to clamped plate problems. The problems are approximated by the nonconforming Morley and Adini element methods in each subregion into which the original region of the discussed problems have been partitioned. On the interfaces between subdomains and at crosspoints of subregions some continuity conditions are imposed. ...

In this paper, we describe the main ideas of the mortar element method combined with H(curl)–conforming finite elements for the numerical approximation of Maxwell’s equations. This method turns out to be a new non–conforming, non–overlapping domain decomposition technique where non–matching grids are allowed at the interface between adjacent sub–domains. We report the results on the method’s co...

We model ferromagnetic effects by using reduced scalar potential. An overlapping domain-decomposition technique is proposed to solve the underlying problem in unbounded domain. In the near-field, adjacent to the ferromagnetic object, we employ finite element discretization, while the far-field, going to infinity, is modelled through Green representation formulas. In this way, we circumvent the ...

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...