A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations

Stevenson, Rob; van Venetië, Raymond; Westerdiep, Jan

doi:10.48550/arxiv.2101.03956

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2021

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“…Such an adaptive refinement might result in unstructured simplicial meshes as in [LSTY21] or in varying spatial meshes associated to certain time steps [SVW21].…”

Section: Applicationsmentioning

confidence: 99%

Interpolation Operator on negative Sobolev Spaces

Diening¹,

Storn²,

Tscherpel³

2021

Preprint

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We introduce a Scott-Zhang type projection operator mapping to Lagrange elements for arbitrary polynomial order. In addition to the usual properties, this operator is compatible with duals of first order Sobolev spaces. More specifically, it is stable in the corresponding negative norms and allows for optimal rates of convergence. We discuss alternative operators with similar properties. As applications of the operator we prove interpolation error estimates for parabolic problems and smoothen rough right-hand sides in a least squares finite element method. 0 that preserves constants on interior simplices. Both properties are not available

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“…Such an adaptive refinement might result in unstructured simplicial meshes as in [LSTY21] or in varying spatial meshes associated to certain time steps [SVW21].…”

Section: Applicationsmentioning

confidence: 99%