From The Telegraph:
"Her Majesty took her husband a birthday card, addressed to “HRH The Duke of Edinburgh” as he continues to recover from surgery at the London Clinic. After a 35-minute visit, she left, looking relaxed and happy, as she shook hands with her physician, Prof John Cunningham, who is in overall charge of the Duke’s treatment. Buckingham Palace said the Duke was “progressing according to plans at this early stage” and is “comfortable and in good spirits”. He is still awaiting the results of tests carried out during an exploratory operation on his abdomen on Friday, and will remain in hospital for another two weeks before “taking a period of convalescence of approximately two months”, the Palace said. Earlier in the day the Earl of Wessex became the Duke’s first visitor since his operation when he spent 20 minutes by his bedside, also taking a birthday card with him. As he left the hospital he was asked how his father was doing, and replied: “Well, thank you.”
The fact that the Duke is feeling well enough to receive visitors suggests he is making a good recovery from his operation.
"Aides had earlier said that members of the Royal family would only visit the Duke if his doctors said he was strong enough to have company. The nature of the Duke's complaint is not known, but doctors decided he should have the exploratory operation following a regular health check carried out in the past fortnight. The Queen dismissed concerns for his health when she visited the BBC on Friday, telling the Today programme presenter John Humphrys he was "not ill".