On the Backward Euler Method for Parabolic Equations with Rough Initial Data
Copyright policy )On the Backward Euler Method for Parabolic Equations with Rough Initial Data
The backward Euler method is applied for the discretization in time of a general homogeneous parabolic equation in weak form. A short proof is given that, with k the time step, the norm of the error at time t is bounded by $Ckt^{ - 1} $ times the norm of the initial data. The result permits application to equations which are already discretized in space.
backward Euler method, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, Numerical solutions to equations with linear operators, discretization in time, Hilbert space, Initial value problems for linear higher-order PDEs, rough initial data, Higher-order parabolic equations
backward Euler method, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, Numerical solutions to equations with linear operators, discretization in time, Hilbert space, Initial value problems for linear higher-order PDEs, rough initial data, Higher-order parabolic equations
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