175 research outputs found
A posteriori error estimates for the Electric Field Integral Equation on polyhedra
We present a residual-based a posteriori error estimate for the Electric
Field Integral Equation (EFIE) on a bounded polyhedron. The EFIE is a
variational equation formulated in a negative order Sobolev space on the
surface of the polyhedron. We express the estimate in terms of
square-integrable and thus computable quantities and derive global lower and
upper bounds (up to oscillation terms).Comment: Submitted to Mathematics of Computatio
Unconditional stability of semi-implicit discretizations of singular flows
A popular and efficient discretization of evolutions involving the singular
-Laplace operator is based on a factorization of the differential operator
into a linear part which is treated implicitly and a regularized singular
factor which is treated explicitly. It is shown that an unconditional energy
stability property for this semi-implicit time stepping strategy holds. Related
error estimates depend critically on a required regularization parameter.
Numerical experiments reveal reduced experimental convergence rates for smaller
regularization parameters and thereby confirm that this dependence cannot be
avoided in general.Comment: 21 pages, 8 figure
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