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math.NA2023★ 1 cited
A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation
Harald Monsuur, Rob Stevenson
We consider an ultra-weak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the `ideal' method yields the best approximation to the…
math.NA2023
A convenient inclusion of inhomogeneous boundary conditions in minimal residual methods
Rob Stevenson
Inhomogeneous essential boundary conditions can be appended to a well-posed PDE to lead to a combined variational formulation. The domain of the corresponding operator is a Sobolev…
math.NA2023
Minimal residual methods in negative or fractional Sobolev norms
Harald Monsuur, Rob Stevenson, Johannes Storn
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and th…