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Displaying 141 –
157 of
157
We prove the optimal convergence of a discontinuous-Galerkin-based
immersed boundary method introduced earlier [Lew and Buscaglia, Int. J. Numer. Methods Eng.76 (2008) 427–454]. By switching to a discontinuous
Galerkin discretization near the boundary, this method overcomes the
suboptimal convergence rate that may arise in immersed boundary
methods when strongly imposing essential boundary conditions. We
consider a model Poisson's problem with homogeneous boundary
conditions over two-dimensional...
We present an improved, near-optimal hp error estimate for a
non-conforming finite element method, called the mortar method (M0). We
also present a new hp mortaring technique, called the mortar method (MP),
and derive h, p and hp error estimates for it, in the presence of
quasiuniform and non-quasiuniform meshes. Our theoretical results,
augmented by the computational evidence we present, show that like (M0), (MP)
is also a viable mortaring technique for the hp method.
In this short note we provide an optimal analysis of finite element convergence on meshes containing a so-called band of caps. These structures consist of a zig-zag arrangement of ‘degenerating’ triangles which violate the maximum angle condition. A necessary condition on the geometry of such a structure for various -convergence rates was previously given by Kučera. Here we prove that the condition is also sufficient, providing an optimal analysis of this special case of meshes. In the special...
We consider a finite element discretization by
the Taylor–Hood element for the stationary
Stokes and Navier–Stokes
equations with slip boundary condition. The slip boundary condition
is enforced pointwise for nodal values of the velocity in
boundary nodes. We prove optimal error estimates in the
H1 and L2 norms for the velocity and pressure respectively.
An optimal part of the boundary of a plane domain for the Poisson equation with mixed boundary conditions is to be found. The cost functional is (i) the internal energy, (ii) the norm of the external flux through the unknown boundary. For the numerical solution of the state problem a dual variational formulation - in terms of the gradient of the solution - and spaces of divergence-free piecewise linear finite elements are used. The existence of an optimal domain and some convergence results are...
The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...
The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart.
However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features
of this system. For this reason, a simplification of this model, called Monodomain problem is quite often
adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in
the presence of applied currents...
The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in...
We consider the analysis and
numerical solution of a forward-backward boundary value problem.
We provide some motivation, prove existence and uniqueness in a function
class especially geared to the problem at hand, provide various energy
estimates, prove a priori error estimates for the Galerkin method,
and show the results of some numerical computations.
Currently displaying 141 –
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157