Optimal-order error bounds of order h^2 plus tau^q are proven for the fully discrete bulk-surface Cahn-Hilliard system with dynamic boundary conditions for BDF methods q=1,...,5, using an almost mass conservation argument.
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A Lagrange-multiplier enhanced evolving surface finite element method provably decreases surface area at every time step while retaining optimal h^k+tau^q convergence for mean curvature flow.
Introduces an admissible minimizing-movement framework for parametric FEM approximations of geometric gradient flows that recovers classical BGN and MDR schemes, adds two new variants, and proves unconditional energy stability.
Proof of optimal H1-norm error estimates for A-stable BDF1/BDF2 full discretizations of Willmore flow using surface finite elements of degree at least 2.
citing papers explorer
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Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
Optimal-order error bounds of order h^2 plus tau^q are proven for the fully discrete bulk-surface Cahn-Hilliard system with dynamic boundary conditions for BDF methods q=1,...,5, using an almost mass conservation argument.
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Structure-preserving Lagrange-multiplier methods for mean curvature flow and their error bounds
A Lagrange-multiplier enhanced evolving surface finite element method provably decreases surface area at every time step while retaining optimal h^k+tau^q convergence for mean curvature flow.
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A minimizing-movement framework for geometric gradient flows with admissible tangential motion
Introduces an admissible minimizing-movement framework for parametric FEM approximations of geometric gradient flows that recovers classical BGN and MDR schemes, adds two new variants, and proves unconditional energy stability.
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Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces
Proof of optimal H1-norm error estimates for A-stable BDF1/BDF2 full discretizations of Willmore flow using surface finite elements of degree at least 2.