We propose new locking-free finite element methods for Biot’s consolidation model by coupling nonconforming and mixed finite elements. We show a priori error estimates of semidiscrete and fully discrete solutions. The main advantage of our method is that a uniform-in-time pressure error estimate is provided with an analytic proof. In our error analysis, we do not use Grönwall’s inequality, so t...

We consider a linear, Schrödinger type p.d.e., the ‘Parabolic’ Equation of underwater acoustics, in a layer of water bounded below by a rigid bottom of variable topography. Using a change of depth variable technique we transform the problem into one with horizontal bottom, for which we establish an a priori H estimate and prove an optimal-order error bound in the maximum norm for a Crank-Nicols...

We present a local exponential fitting hybridized mixed finiteelement method for convection-diffusion problem on a bounded domain with mixed Dirichlet Neuman boundary conditions. With a new technique that interpretes the algebraic system after static condensation as a bilinear form acting on certain lifting operators we prove an a priori error estimate on the Lagrange multipliers that requires ...

Boundary or interior layers are usually highly directional solution features. Thus, suitable anisotropic meshes, reflecting the directional features of the solution, provide the basis for the most efficient numerical approximation. Anisotropic mesh design strategies based upon a priori analysis have been developed for a variety of PDE problems and discretisations. On the other hand a posteriori...

We introduce a discrete network approximation to the problem of the effective conductivity of the high contrast, highly packed composites in three dimensions. The inclusions are irregularly (randomly) distributed in a hosting medium, so that a significant fraction of them may not participate in the conducting spanning cluster. For this class of spacial arrays of inclusions we derive a discrete ...

A local a priori and a posteriori analysis is developed for the Galerkin method with discontinuous finite elements for solving stationary diffusion problems. The main results are an optimal-order estimate for the point-wise error and a corresponding a posteriori error bound. The proofs are based on weighted -norm error estimates for discrete Green functions as already known for the ‘continuous’...