[HTML][HTML] Goal-oriented adaptive space-time finite element methods for regularized parabolic p-laplace problems

B Endtmayer, U Langer, A Schafelner - Computers & Mathematics with …, 2024 - Elsevier
We consider goal-oriented adaptive space-time finite-element discretizations of the
regularized parabolic p-Laplace problem on completely unstructured simplicial space-time …

Additive Schwarz methods for semilinear elliptic problems with convex energy functionals: Convergence rate independent of nonlinearity

J Park - SIAM Journal on Scientific Computing, 2024 - SIAM
We investigate additive Schwarz methods for semilinear elliptic problems with convex
energy functionals, which have wide scientific applications. A key observation is that the …

Additive Schwarz methods for fourth-order variational inequalities

J Park - Journal of Scientific Computing, 2024 - Springer
Fourth-order variational inequalities are encountered in various scientific and engineering
disciplines, including elliptic optimal control problems and plate obstacle problems. In this …

Two-Level Overlapping Schwarz Preconditioners with Universal Coarse Spaces for th-Order Elliptic Problems

J Park - SIAM Journal on Scientific Computing, 2024 - SIAM
We propose a novel universal construction of two-level overlapping Schwarz
preconditioners for th-order elliptic boundary value problems, where is a positive integer …

Subspace correction methods for semicoercive and nearly semicoercive convex optimization with applications to nonlinear PDEs

YJ Lee, J Park - arXiv preprint arXiv:2412.17318, 2024 - arxiv.org
We present new convergence analyses for subspace correction methods for semicoercive
and nearly semicoercive convex optimization problems, generalizing the theory of singular …

Two-level overlapping Schwarz preconditioners with universal coarse spaces for th-order elliptic problems

J Park - arXiv preprint arXiv:2403.18970, 2024 - arxiv.org
We propose a novel universal construction of two-level overlapping Schwarz
preconditioners for $2 m $ th-order elliptic boundary value problems, where $ m $ is a …