Affiliation:
1. Department of Mathematical Sciences , Norwegian University of Science and Technology , Trondheim , Norway
2. Institut für Angewandte Mathematik , TU Graz , Graz , Austria
Abstract
Abstract
Reconstructing the pressure from given flow velocities is a task
arising in various applications, and the standard approach uses the
Navier–Stokes equations to derive a Poisson problem for the pressure p.
That method, however, artificially increases the regularity requirements
on both solution and data. In this context, we propose and analyze two
alternative techniques to determine
p
∈
L
2
(
Ω
)
{p\in L^{2}(\Omega)}
. The first is an
ultra-weak variational formulation applying integration by parts to shift
all derivatives to the test functions. We present conforming finite element discretizations and prove optimal
convergence of the resulting Galerkin–Petrov method. The second approach
is a least-squares method for the original gradient equation, reformulated
and solved as an artificial Stokes system. To simplify
the incorporation of the given velocity within the right-hand side,
we assume in the derivations that the
velocity field is solenoidal. Yet this assumption is not restrictive,
as we can use non-divergence-free approximations and even
compressible velocities. Numerical experiments confirm
the optimal a priori error estimates for both methods considered.
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
1 articles.
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