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We consider the Euler-implicit discretization of a class of nonlinear and possibly degenerate parabolic equations. Here we discuss some linear iterative schemes to approximate the solutions to the resulting time-discrete equations. The schemes rely on a splitting strategy: by adding new unknowns, the nonlinear terms only appear in algebraic equations. For the resulting system, we present different linearization schemes, and discuss their convergence, from both theoretical and numerical point of view.

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Splitting-Based Linearization Schemes for Doubly Degenerate Parabolic Problems

  • 会议论文

  • 发表日期：

    2025年

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  • Ayesha Javed,
  • Koondanibha Mitra,
  • Iuliu Sorin Pop

摘要

We consider the Euler-implicit discretization of a class of nonlinear and possibly degenerate parabolic equations. Here we discuss some linear iterative schemes to approximate the solutions to the resulting time-discrete equations. The schemes rely on a splitting strategy: by adding new unknowns, the nonlinear terms only appear in algebraic equations. For the resulting system, we present different linearization schemes, and discuss their convergence, from both theoretical and numerical point of view.